Actually, yes! Shakespeare wrote a number of stage directions, though they were never exactly... thorough. For example, at the opening of Hamlet, Shakespeare writes:
FRANCISCO at his post. Enter to him BERNARDO.
Stage directions written by Shakespeare are usually like this: short, sweet, and to the point, if present at all. The reason for this is pretty simple: he didn't really need to write down stage directions when he himself was the director! Most of the time, they appear to be more... notes, or reminders.
This actually puts a number of... stranger and odder stage directions into a more interesting light. There are stage directions like:
Exit pursued by a bear (A Winter's Tale)
Enter a messenger with two heads and a hand (Titus Andronius)
However, it appears that much of the time, the company itself wrote in stage directions:
After writing out a manuscript, Shakespeare (or a professional scribe) made a copy of it in which obvious errors were corrected. The two versions had special names: the original manuscript was the "foul papers" because of the blots and crossouts on it. The new version was called a fair copy. It was submitted to the Master of Revels, a government censor who examined it for material offensive to the crown. If approved, the fair copy became known as a prompt copy, which the actors used to memorize their lines. The acting company bought the prompt copy, gaining sole possession of it, after paying the writer. The company then wrote in the stage directions (exit, enter, etc.).
It appears that Shakespeare wrote in some small (and often humorous) stage directions as reminders, and then the remainder of the stage directions were filled in by the publisher before being passed to the actors for memorization.
