Originally, what follows was a section of the question. However, at the suggestion of Gallifreyan, I've migrated it to this answer. It's quite long, and it includes works by others as well as a little original analysis of mine that I've done for the case of Easy Rider.
Summary of the research conducted so far
'Book titles and their articles' by Leszek Berezowski (here)
This author is a linguist who actually wrote a whole book on how to understand article-free noun phrases (The Myth of the Zero Article, here). The paper under discussion deals with non-fiction, and particularly with titles that feature of-phrases (Psychology of Reading vs. The Psychology of Reading vs. A Psychology of Reading), and so is not that relevant to most of my examples. Nevertheless, since one of my examples features an of-phrase, I should briefly explain what the paper says.
Basically, Berezowski says that the contrast between The Psychology of Reading and Psychology of Reading is this. In the former, we have a narrowing down of the field of study from everything that can be asked about reading to specifically its psychological aspects. In contrast, in the latter, there is no such narrowing down. Just as
soup of the day is not an aspect of the day but a dish named after its French model, Journal of Linguistics is not a subfield of the study of language but a periodical devoted to language research,
so the authors of Psychology of Reading
do not view psychology as merely one of the angles at which the process of reading can be researched but treat psychology of reading as a fully fledged discipline in its own right. In other words the title proclaims that the book will survey an entire existing branch of knowledge or create a new paradigm of research.
This, however, does not explain Tropic of Cancer. Of course, this title is a play-on-words that needs a bit of explaining. In the first place, in its 'standard' meaning (which by the way always includes the definite article), the Tropic of Cancer, also called the Northern Tropic, is 'the most northerly circle of latitude on Earth at which the Sun can be directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted toward the Sun to its maximum extent' (source). Its southern counterpart is called the Tropic of Capricorn. From the same source:
When this line of latitude was named in the last centuries BC, the Sun was in the constellation Cancer (Latin for crab) at the June solstice, the time each year that the Sun reaches its zenith at this latitude. Due to the precession of the equinoxes, this is no longer the case; today the Sun is in Taurus at the June solstice. The word "tropic" itself comes from the Greek "trope (τροπή)", meaning turn (change of direction, or circumstances), inclination, referring to the fact that the Sun appears to "turn back" at the solstices.
As far as the book, its author Henry Miller said the following (here):
Do you know why I called my first book Tropic of Cancer? It was because to me cancer symbolizes the disease of civilization, the endpoint of the wrong path, the necessity to change course radically, to start completely over from scratch … Yes, from scratch, no question about it, for better or for worse … What I want is to halt evolution, to go backward down the path we have taken, to back to the world before childhood, to regress, regress, regress, further and further, until we get to the place we have only lately left behind, where culture and civilization do not figure … It is time we start to think, to feel, to see the universe in a way that is uncultivated, primitive—but this is also without but this is also without doubt the most difficult thing in the world to do.
There is even more that can be said: cancer means crab, which is 'the only living creature which can walk backwards and forwards and sideways with equal facility.' A nice discussion can be found in the blog post 'Naming Tropic Of Cancer', here.
But for our purposes, note that neither the 'regular' meaning nor Henry Miller's wordplay fit Berezowski's paradigm. In the regular usage, the narrowing down goes the opposite way than in Berezowski's examples: there are two tropics, and the of phrase specifies which one. To fit Berezowski's paradigm, we would need to interpret [the] Tropic of Cancer as referring, in the first place, to the general topic of 'cancer', and then to a narrowed-down topic of tropic as it concerns cancer. And that, of course, makes no sense in either the regular or Henry Miller's sense of the phrase. In this respect Henry Miller's meaning is similar to the regular meaning: the turning or regression he is talking about is not a narrowing down of the topic of the disease of cancer, but rather something like a regression caused by that disease. Alternatively, this turning is like the walk of a crab.
One could argue that Miller is dropping the article as a hint that he's not talking about the Northern Tropic but about something else. I don't find this persuasive. Even if the definite article were retained, I don't think readers would need a hint to consider the possibility that the title is somehow symbolic or a play-on-words. Conversely, I don't think there's much symbolism in the title of the movie Moon, and yet the usually required definite article is dropped. All said, I very much doubt that Miller's primary consideration in dropping the article was to make sure people consider what else his title might mean other than the Northern Tropic. Maybe that was part of it, but I can't believe that's the full explanation.
'Riding a Straight Line between The Wild One and Wild Hogs' by Thomas Goodmann
The following passage makes a comparison between the titles of the movies The Wild One and Wild Hogs,1 specifically as far as what effect the inclusion or exclusion of the article has on them:
1True, Wild Hogs doesn't belong to my paradigm, since hogs is a count noun in the plural and so it could appear without a determiner even in everyday speech and writing. However, perhaps any insight gained in this case could be helpful with my examples as well.
The title of the film likewise performs work of cultural containment when read against its precursory text. Like many narratives of heroism and anti-heroism, The Wild One instantiates the exceptional—indeed, marginal—masculinity of a single member, Johnny Strabler, among a group of men, a trope in narrative evident since Gilgamesh and the Odyssey, and extant in American culture from James Fennimore Cooper’s novel The Deerslayer (1841), to Michael Cimino’s film The Deerhunter (1978), and beyond. In the case of Benedek’s film, the plural title, lacking a definite article, emphasizes the corporate community of identity in the non-gang relations of the four Wild Hogs, each supporting one another, yet not within a hypermasculinated group, such as a motorcycle gang, so that each is not code-bound to prioritize the group over the self, and is therefore free to pursue his own pursuits, while maintaining membership. It is significant then that when Damien Blade asks the Hogs, “What do you call yourselves?” they answer initially by giving their first names, so that Blade reformulates the question to elicit their group identity as “Wild Hogs.” The non-gang’s interrelations emphasize somewhat fluid and empathic masculine identities, as opposed to the comically flattened characters and more strictly stratified relations of the “real” motorcycle gang, whose stereotyped identities signal their outmoded masculinity, replete with clubhouse/bar, ape-hangers and loud pipes, coercion, and threat of violence. And as we will see, a latent impulse of homosexual violence erupts from gang member Red, only to be slugged into silence by Blade.
(source, boldfaced emphasis mine)
Unfortunately, even supposing this explanation completely explains the reason why the filmmakers chose to go with Wild Hogs rather than The Wild Hogs, this explanation does not easily carry over to my examples. The suggestion is that the lack of the definite article emphasizes that 'each [member of Wild Hogs] is not code-bound to prioritize the group over the self'. But in my examples, the relevant nouns do not denote a group, except possibly in Animal Farm; but even that title is not the name of a group.
Three blog posts
'David V. Appleyard's Guide to Article Usage in English' (here)
There is one mention of book/movie titles:
To give added punch, articles are often dropped in the titles of books, movies, music and other works of art. (Example: Journey into Hell sounds even more thrilling than The Journey into Hell.)
For our purposes, this is almost an empty statement. Added punch simply means that the author thought it sounded better, which of course the author did, or else he or she would not have dropped the article. The question is why does dropping the article have that effect.
'The Huge Impact of ‘The’ in Movie Titles' (here).
This contains an opinion regarding my question:
And finally, sometimes the absence of “The” gives a movie title an unsettling aura. It doesn’t sound wrong, but it feels like there’s something missing or just a little off-kilter about it.
Psycho, Alien, Aliens, Predator, Blade Runner, Gladiator
Without “The,” none of these titles point to a definitive subject. They become rather subjective and even more fascinating as we explore their full implications as the story unfolds.
The main comment here is that these titles would also not point to a definite subject if they were preceded by the indefinite article.
'The "the" is THE best thing to happen to the titles of the movies in the theaters' (here)
Unfortunately I didn't find anything useful in this blog post, and I'm only mentioning it because 1. it sounds as if it should be relevant, and, more importantly, because 2. it disputes the claim that the title is 'punchier' without the definite article. (Provided, of course, the whole post isn't tongue-in-cheek, which it may well be.)
An explanation from wordreference.com
Here is an attempt at an explanation (in the context of titles of paintings), which however I don't think succeeds ('Usage of articles in the titles of paintings', here).
Japanese Vase - a Japanese vase chosen at random from many examples probably because (i) it was convenient and/or (ii) it appealed to the artist.
A Japanese Vase - An example, probably typical, taken from many Japanese vases.
The Japanese Vase - (i) the definitive example of vase of Japanese origin or (ii) the Japanese vase that is associated with some commonly known event/person/history/style/etc. (iia) used where the painting is really famous: “The Mona Lisa,” “The Sunflowers,” “The portrait of Whistler's Mother.”
The contrast between the A and The versions is clear enough, but I'm not sure I understand the explanation of the contrast between Japanese Vase and A Japanese Vase. According to the explanation, both Japanese Vase and A Japanese Vase refer to Japanese vases chosen from many other vases. Could not the former be 'a typical example' of a Japanese vase? Could not the latter be a vase that was either convenient or that appealed to the artist?
Questions on StackExchange
Over on the English Language and Usage StackExchange (EL&U SE), there was the following recent question: Zero articles in movie and book titles (which, frankly, was what motivated me to pose this question on the Literature SE). The accepted answer there said
Consider the case when someone shouts out your name: you turn to look, without concerning yourself whether they have defined fully who you are. The essential quality of the communication is that both sides understand what is meant, in the minimum of words.
This is along the lines of the 'saving space' explanation of headlinese, and as such I find it unconvincing. The title of a film or a novel is part of the artistic expression of the work, and can color the entire reading of it; I simply do not believe that efficiency is the primary consideration of literary authors when choosing the title of their work.
Another answer said that
Much of the time a title, especially that of a book or movie, is meant to entice, describe, but also leave a question in the air, so to speak.
This is close to the explanation given in the 'unsettling absence' passage, above. But is it really true that Taxi Driver sounds more mysterious than The Taxi Driver? And if it sounds more 'enticing' without the article, is there anything one could say as to why that is so?
There was a missed opportunity to address this issue in another question (Usage of “a” and “the” in titles) on EL&U SE, as it was not discussed why Apple should be without an article.
Yet another question, Articles in movie or book titles: noun vs. adjective, turned on playing up ambiguity in the titles, which, as I said, I don't believe is what's happening in my examples.
The main difficulty in applying the discussion of band names to my question is the same as it was with the discussion of the movie Wild Hogs: both band names and motorcycle gang names are names of groups of people. This is just not the case in my six examples, and thus much of the discussion surrounding band names is irrelevant to my question. This is the case with the discussion on Grammar Girl (here) as well:
The bottom line is that fans are likely to think a band name should have the in the name if they view the name as describing the members rather than being collective. In other words, we probably don’t call it The Led Zeppelin because we simply think of Led Zeppelin as the name of the band, and don't think of it as describing the band, but we probably do call them The Eagles because we’d say “Don Henley is an Eagle.”
This is interesting, but not relevant to my question.
Here the difficulty is that brand names have a very particular purpose which is not shared by titles of novel and movies. The Grammar Girl says the following :
One reason for [dropping the articles from brand names] is to save space and characters in Web addresses and tweets, but another reason, according to two marketing experts quoted in the article, amounts to the idea that a singular count noun without an article sounds like something more personal than a mere object or corporation.
This is again interesting, but not at all relevant to my questions. There is no issue of presenting something as personal vs an object or a corporation in my six examples.
There are some posts on the web one might hope would provide some insight, but that don't. An example is 'When should articles be avoided in titles?' on Quora here
An attempt at answering my question in the case of Easy Rider
In a documentary, the film's director and co-star Dennis Hopper explained the meaning of the term an easy rider as follows:2
An easy rider is a person that is not a pimp, but he lives off a woman; he lives off a whore. He's her easy rider. He's the one that she loves and she gives money to. He doesn't pimp her, but he's her easy rider.
2It was the screenwriter Terry Southern who came up with the title. Dennis Hopper claimed this was actually Southern's only contribution to the film, despite being listed as a co-screenwiter together with the film's co-stars Hopper and Peter Fonda; see here.
I found Roger Ebert's original 1969 review of the film quite useful. The suggestion there seems to be that while the middle class is prostituting itself to the establishment, the so-called non-conformists like the Fonda and Hopper characters (Wyatt and Billy) are just as bad. They have also sold out; they also are prostitutes, or, more precisely, they are those who freeload off prostitutes: the 'easy riders'.
Personally, I also have other associations with the term an easy rider: it could refer to the type of motocycle that the movie made famous, as being easy to ride (though they absolutely were not in reality); or perhaps it could refer to the kind of poeple who ride them, because they ride them effortlessly (though actually they were not that easy to ride, especially at long distances). Both interpretations would serve to identify Wyatt and Billy as those who are the ‘easy riders’ here in the other meaning of that term (“freeloading lovers of prostitutes”).
Now, about the articles. Because there are two 'easy riders' in the movie, neither The Easy Rider nor An Easy Rider seem suitable (there are probably other reasons as well, but this one is arguably sufficient on its own). This leaves us with the following choices: (1) The Easy Riders, (2) Easy Riders, and (3) Easy Rider.
Option (1) sounds like the name of a motorcycle gang. If that association were made, it would be a very relevant one in this particular movie. As Roger Ebert wrote,
“Easy Rider” takes the gang leader (Fonda) and condenses his gang into one uptight archetype (played by director Hopper.) It takes the aimless rebellion of the bike gangs and channels it into specific rejection of the establishment (by which is meant everything from rednecks to the Pentagon to hippies on communes).
However, in the context of the movie, the Easy Riders would not make sense as a name for this skeleton band. For most of the movie, Wyatt and Billy think they are being very clever and free and so on; it is only at the very end that one of them realizes it's not so (the 'We blew it' line of Fonda). Therefore, for most of the movie, if they were to name themselves at all, it would be something more positive. I would think calling themselves “the Easy Riders” would be too cynical and out of character.
Option (2) could also be a gang name (like Wild Hogs), in which case what I just said about option (1) applies. Alternatively, option (2) may suggest there are other 'easy riders.' And on the one hand, there are: there are no doubt countless others who are trying to avoid the various negative aspects of conventional life, but end up selling themselves out in one way or another. But on the other hand, the movie clearly emphasizes individuality and individualism. There are many kinds of sellouts, but in this particular movie we probably don't want to suggest it's some sort of homogeneous mass.
This leaves us with option (3). It may seem we have now arrived at it by a process of elimination, once we realized that the other four possibilities are all unsuitable for various reasons. However, we are actually not done yet. After all, this option carries its own set of connotations and associations, which could concievably make it even more unatractive than the other options. So we have to now analyze this option.
It is the most basic of all the options, in the sense that it involves the base form of the noun. Without any marks of definiteness or indefiniteness, this option comes the closest to denoting 'the pure concept of easy-riderness'. It does so without having to use words such as riderness or ridership or riding, which, I will consent to admit, obviously sound plain ugly, at least if one tries to use them in this particular title.
Another way to get at 'the pure concept of easy-riderness' is to consider what kinds of ambiguity are present. Here we might have an ambiguity of definiteness: it's simultaneously 'an easy rider' and also 'the easy rider'. (Perhaps it's even also 'easy riders' as well as 'the easy riders'—indicating an ambiguity of the grammatical number—if the base form is looked at abstractly enough. I admit this sort of ambiguity seems like a stretch in this case, however.) At any rate, the article-free base form perhaps manages to convey at least some of these multiple meanings simultaneously.
I've presented several attempts to understand the omission of determiners in titles such as Animal Farm, Little House on the Prairie, Tropic of Cancer, Easy Rider, Taxi Driver, and Rear Window. In the case of Easy Rider, I eliminated all other possibilities on various grounds, and suggested that the article-free base form expresses the pure concept behind all of the variations of that form whose definiteness is fixed (an + singular, the + singular, the + plural, no article + plural).
Even if that last suggestion of mine works for Easy Rider, I don't think it works always. In particular, I can't see how it would work for Little House on the Prairie. Incidentally, that title is the one whose explanation is perhaps needed most urgently, because the adjective little carries a special connotation when used without an article. For example, She has little time for that means she has basically no time, whereas She has a little time for that means she can indeed spare some time. True, little can't be used literally like that in the construction that appears in the title, but here we are talking about language whose rules have been relaxed and where associations are much more free-flowing.