Ok, here's the game. Find a quote in one play that looks like it's a reference to another one. Chances are it wasn't, but then again who really knows, right?
The most obvious one, perhaps, is when Macbeth says that he will not "play the Roman fool" and fall upon his sword....exactly like Brutus does at the end of Julius Caesar. That one only half counts, since it's obviously more a historical reference than Shakespeare directly referencing himself. (There's also the part in Hamlet where Polonius speaks of having played Caesar.)
I thought of this thread during AYLI it the other day, since the character playing Jaques also played Bottom last year, and there's a Jaques line where he says "If it do come to pass that any man turn ass...." which of course is exactly what happens to Bottom.
Lastly, I think it's funny to imagine that Amiens' song:
Blow, blow, thou winter wind.
Thou art not so unkind
As man's ingratitude;
Thy tooth is not so keen,
Because though are not seen,
Although thy breath be rude.
Is actually a reference to Lear:
Blow, winds, and crack your cheeks! rage! blow!
But of course I realize that would be pushing my luck :). Can't you just imagine Lear on the heath breaking out into song?