A favorite Shakespeare movie moment of mine is Mercutio's Queen Mab speech in the most recent Romeo and Juliet. I absolutely LOVE that interpretation of it...just the right edge of madness.
Peter, the wooing scene from Branagh's Henry V is one of my favorites, too.
I also especially like the Army kid's rendition of the St. Crispin's Day speech in Renaissance Man. Not exactly the same thing, but it's a wonderful moment!
We read R&G Are Dead in my English class this year...great! My friends and I go into the question game every now and then.