Best film version of a Shakespeare play: [ooh, this is a tough one]
I think I will punt...my favorite is the Kenneth Branagh / Emma Thomson / Denzel Washington Much Ado About Nothing. It is a rollicking good time. (aside: I recall a note from English class that in Shakespeare's time, "Nothing" was pronounced so it sort of rhymed with "noting" which was a word that meant eavesdropping....)
I also read about a version of Richard III that starred Ian McKellan that was set in 1920's gangster Chicago. Not sure if it was a movie or a stage production. Sounds really interesting.
There are so many great films, Olivier as Hamlet, Brando in Julius Caesar, Welles' Macbeth, I wouldn't know where to choose.