I've watched the Gibson, Branagh, and Tennant versions over and over. Probably all of you have seen the first two, but if you haven't seen Tennant, you should watch his rendition.
It's trimmed down a bit from the original, which I didn't notice the first time I watched it because it still flows seamlessly. Actually, I like the cut better than the original: it leaves out the long, repetitious list of ills that makes the speech lose forward momentum.
I also like his exhaustion. Tennant's Hamlet yearns for sleep, a symptom of his depression. I love the way he says "awry," and how he's cut off by Ophelia's entrance: maybe Hamlet really did have more to say on the subject.
I watched a few other versions and mostly didn't like them: Lawrence Olivier's was stilted, Kevin Kline's was underwhelming (although his little smile after "to sleep" was cute), and Richard Burton's was unnatural. Derek Jacobi did a good job at a frenetic, hysterical Hamlet, which isn't my preferred interpretation but mixes things up interestingly:
[For all you Whovians out there, a fun bit of trivia: Derek Jacobi played the Master in the episode "Utopia," and in his version of Hamlet, Ophelia was played by none other than Lalla Ward, known best as Romana.]
I think that before the death of his father Hamlet was a happy person. He was friends with hilarious people at school and he loved to watch players. This speech may be the first time that he seriously contemplates the idea of suicide. Some readers/viewers complain that Hamlet is "emo" and teenager-ish in his constant complaints, but one must appreciate how good his life probably was before his father died: he had friends and a loving family, and he was a prince secure in his future. Claudius destroyed every aspect of his happiness, rending his family apart and even preventing him from returning to school. Then his father's ghost laid the task of revenge on him, making it impossible for Hamlet to grieve normally and rebuild his life. No wonder he desperately grasped for an easier option.
Of course, you can argue about whether or not he's sincere. If he knows he's being watched by Polonius and Claudius, he may just be acting to the full extent of his grief for their benefit, playing the madman. If he knows he's being watched by Ophelia, he may be pleading for sympathy or trying to renew their love. But if he believes that he's alone, then his speech is a cry to the universe:
Shall I go on?
Must I go on?
And by a sleep to say we end the heartache and the thousand natural shocks that flesh is heir to. 'Tis a consummation devoutly to be wished.