The best stage production of Hamlet I have seen so far was that of Calixto Bieito, in a 2003 production for the Edinburgh Festival, which I caught in Birmingham in  September 2003.
This production set the play in a piano lounge, with chrome-and-black-leather furniture and the participants wearing modern dress.   Horatio (Karl Daymond) played the piano, and like it, was dressed entirely in white.  The music was chosen very well, with Bach before and after “To be or not to be”.   The other music was mostly jazz and the music expected of a piano lounge.   At the moment when Hamlet got Rosenkrantz and Guildenstern to confess they were working for Claudius, Hamlet pointed to Horatio at the piano, who played the theme from Dragnet (Da-ta-da-daaaa).  The music seemed to intensify the emotions of the play, and the modern dress and setting led this to seem like a Eugene O’Neill psychodrama.
Prior to seeing this version, I’d only ever considered two broad interpretations of Hamlet – the personal (Should I avenge my father’s murder?) and the political (Can I kill the King?).   This production emphasized, in between the personal and the political, the family dimensions – hence the feeling that O’Neill had written and directed it.   Adding to this feeling was the acting-out of some of the accusations made – eg, of Polonius killing his daughter (which revulsed her), and of Hamlet raping Ophelia.
The family setting was further emphasized by the absence of any attendant servants, lords or ladies, and the absence of regal attire.   The single lounge room set, with a grand piano and a drinks cabinet, also added to the cosy, biedermeier feeling.   Here, there were scenes of Claudius and Gertrude playing sexy games together in their pajamas.  As in any 20th century American drama, drinks played a large part in action:    “Who’s Afraid of Virginia Woolf”, with soliloquies.
A very nice touch was Rosenkrantz and Guildenstern arriving dressed as the Blues Brothers – dark suits, sunglasses, and briefcases.   Overall, this was a superb production.  The theatre, the Birmingham Repertory Theatre,  was about 25% full, with perhaps 400 people present.
Another modern interpretation of Hamlet, as a German comedy, was reviewed here.