I'm reasonably certain that Irving's major inspiration for Rip van Winkle was the German folktale Peter Klaus (text here). Almost all the analyses I've read give it precedence over other works (Karl Katz, for instance is a similar, though less-well-documented story). There are many similarities that quickly indicate some connection:
The main character disappears for twenty years:
"Ah, poor man, Rip Van Winkle was his name, but it's twenty years since he went away from home with his gun" - Rip van Winkle
"It is now twenty years since his goats returned without him" - Peter Klaus
Rip/Peter witnesses a supernatural game of bowling:
On a level spot in the centre was a company of odd-looking personages playing at nine-pins. - Rip van Winkle
Here were twelve knights, who, without so much as uttering a syllable, were very gravely playing at nine-pins - Peter Klaus
Upon his return, he asks about whether his old friends are still around:
Rip bethought himself a moment, and inquired, “Where’s Nicholas Vedder?”
. . .
“Where’s Brom Dutcher?”
. . .
“Where’s Van Bummel, the schoolmaster?” - Rip van Winkle
. . . to get rid of his questioners he mentioned the first name that occurred to him, “Kurt Steffen?”
. . .
“Velten Meier?” - Peter Klaus
Even more specifically, it is mentioned that Vedder and Steffen are both "in the churchyard".
This is all besides the fact that both stories follow the same pattern:
- Man lives in a small town ("a small village"/"the peaceful village of Sittendorf") by the mountains ("the Kaatskill mountains"/"the Kyffhaeusen mountains").
- Man walks in the mountains and follows someone ("a short square-built old fellow"/"a boy") to witness men playing nine-pins.
- Man drinks wine and falls asleep for decades.
- Man wakes up and returns to his town. He eventually meets his daughter (Judith/Maria).
This collection of folk-tales (The German Novelists) has a slightly different text, but all of the above connections are the same (although "Velten Meier" is "Valentine Meier", and the boy is a groom tending wild horses).
Even if all of the above were not the case - which they are - there is an even more compelling reason to indicate that Peter Klaus is the main source of inspiration for Rip van Winkle. Irving ends his tale with a humorous note:
The foregoing Tale, one would suspect, had been suggested to Mr. Knickerbocker by a little German superstition about the Emperor Frederick der Rothbart, and the Kyffhäuser mountain: the subjoined note, however, which he had appended to the tale, shows that it is an absolute fact, narrated with his usual fidelity
The German Novelists notes that "similar tales of enchantment" surround the long-dead Emperor Barbarosa (the same person as Frederick der Rothbart), who holds court under the Hartz mountains. I'm reasonably certain that Irving's addendum is a nod to these stories, and, by extension, to Peter Klaus.
Furthermore, Staley's Rip van Winkle's Odyssey states
Irving himself admitted that he drew on the tale of Peter Klaus in creating Rip Van Winkle7
7 In W. Irving, Bracebridge Hall, ed. H. F. Smith (Boston, MA, 1977), 247, in a sketch titled ‘The Historian’, Irving answers the charges of ‘plagiarism’ and asserts that he ‘had considered popular traditions of the kind as fair foundations for authors of fiction to build upon’.
I do not have the text and so cannot verify this myself, but it seems that if Irving explicitly acknowledged that Peter Klaus was the inspiration, it most likely was.
Furthermore, The Original Knickerbocker: The Life of Washington Irving states
As Irving admitted whenever asked (and even inserted as a postscript in the 1848 edition), he drew upon a popular German folk tale, "Peter Klaus", for the central theme of his story.
This could just mean the postscript I cited above, but I'll try to find a text of the edition. This isn't just word-of-author evidence; it's accompanied by strong textual parallels.