Hamlet is a powerful play with many exciting performances. Here you'll find a full stage performance along with film versions by Laurence Olivier, Richard Burton, and Christopher Plummer.
Directed by: Peter Bloedel Scene Design: Peter Bloedel Costume Design: Emily Kimball Lighting Design: Jake Yenish Sound Design/Original Music: Benji Inniger

Other YouTube versions of Hamlet that are notable, but not stage performances:

Laurence Olivier's Hamlet

Christopher Plummer's Hamlet

Oregon Shakespeare Festival did a 1954 production of Hamlet and this YouTube compilation is the entire audio of that production overlayed onto the last remaining productions photographs from that performance. 

Richard Burton's Hamlet | In this production, the language is king. Richard Burton trained himself to speak in a very specific style and it shines in this production. The video quality is not fantastic, but this video is a great example of the power of Shakespeare's language.