{In No Particular Order}
Best "Romeo & Juliet" - Franco Zefferelli's 1968 film
Best "Hamlet" - Laurence Olivier's 1948 film
Best "MacBeth" - Roman Polanski's 1971 film
Best "Henry V" - Kenneth Branagh's 1989 film
Best "Richard III" - Laurence Olivier's 1955 film
Best "Othello" - Stuart Burge's 1965 film
Romeo and Juliet - honestly, I have to side with Baz Luhrmann's film. I'm not generally a fan of Lurhmann but, unlike Zeffirelli's film, his R&J can actually act, and look like they are in love - both kind of crucial.
Hamlet - Branagh, although it's not perfect - if he had cast another actor (i.e. Mark Rylance, who was brilliant on stage a few years earlier) it could have been - but the rest of the cast and the sumptuous production puts it over the top.
Macbeth - Kurosawa's Throne of Blood. Choosing only from 'straight' adaptations, Polanski's by far.
Henry V - Olivier, although it's actually my least favourite of his big three Shakespeare films.
Othello - Oddly, I have never read this play OR seen an adaptation of it... I should fix this!
My favourite adaptations of plays you don't mention are the flawed but beautiful 1935 A Midsummer Night's Dream and Julie Taymor's striking 1999 Titus (her 2010 adaptation of my favourite Shakespeare, The Tempest, is also very good and underrated).