Most Shakespeare movies are pretty lousy and aren't worth watching. He's been adapted to the screen more than 1,100 times, because his works are in the public domain. He's probably the only bankable writer which studios can use for free and people have heard of. That means there's more diversity of interpretation to performances of his plays than those of any other author. That also means one has to sort through a lot of dreck to find gold.
If I were to pick the best screen adaptations of Shakespeare, not counting Akira Kurosawa's Ran or Throne of Blood because they only make use of the plots, I'd rank them:
1.Hamlet 1996 by Kenneth Branagh
2.Othello 1952 by Orson Welles
3.Julius Caesar 1953 with John Gielgud
4.Henry V 1989 by Kenneth Branagh
5.Macbeth 1971 by Roman Polanski
6.Titus 1999 with Anthony Hopkins
7.Richard III 1995 with Ian McKellen
8.Much Ado About Nothing 1993 by Kenneth Branagh
9.The Taming of the Shrew 1967 with Elizabeth Taylor
10.Chimes at Midnight 1965 by Orson Welles
11.A Midsummer Night's Dream 1996 by the Royal Shakespeare Company
12.Twelfth Night 1988 by Kenneth Branagh
For the rest, I'd mostly go with the complete works of Shakespeare series performed for British television by the RSC from '78-'85, and which every library should have a copy of. However, I haven't seen the new Coriolanus and Macbeth which from all accounts sound very good. The Orson Welles Macbeth looks promising, and I generally hate Peter Brook, Laurence Olivier, or Zeffirelli productions, which most other's seem to love.