Forbidden Planet (Sci-fi "The Tempest") - Not a faithful adaptation.

Hamlet (Olivier) - I'm not a huge fan of this version's "to be or not to be" and it's a bit more presentational than modern audiences would care for, but it's reputation is well earned. I liked Eileen Herlie's Gertrude.

Hamlet (Zeffirelli/Gibson) - Overshadowed by Olivier's and Branagh's version, this one is very strong. By far, my favorite Ophelia. If you don't have enough patience for Branagh's, let alone multiple versions, this would be the one to watch, though it had the same problem the Olivier Hamlet did - the inexplicable interpretation and insertion of the Oedipus complex. The film also had a lot of intensity.

Hamlet (Branagh) - This one is going to be required watching for generation if only because it's a reference version. If you have enough patience, but little enough that you're only going to watch one Hamlet, this would be the one to watch.

Hamlet (Almereyda/Hawke) - Very underrated. Hawke is the closest in age of the easily available versions, and Murray's Polonius is great casting.

Henry V (Branagh) - Just incredible artistry from acting to production. Very accessible. If you're only going to watch one film of a Shakespearean play, this is the one to watch.

Love's Labour's Lost (Branagh) - Disappointing.

Macbeth (Polanski) - Gritty, bloody, and awesome. Great "Out, out damned spot" speech.

Merchant of Venice - Pacino (also Pacino's Looking for Richard, while not what you'd consider an adaptation, is interesting)

A Midsummer Night's Dream (Hoffman/Kline/Pfeiffer) - I don't get the hate on this. It's decent, but not great.

Much Ado About Nothing (Branagh) - Like Branagh's Henry, this is a great adaptation of the play to film. Good lord Kate Beckinsale was beautiful. Also has a Keanu performance, though I'd probably stop short of calling the performance good. Denzel's amazing in it, though.

O (Blake Nelson/Hartnett) - Modernized Othello, re-cast in a school setting. I liked it, but it's been a while so I'd recommend the Parker/Fishburne/Branagh version first.

Othello (Parker/Fishburne/Branagh) - Very well acted and produced. I have no reservations recommending this as a film version of the play.

Richard III (Loncraine/McClellen) - It's been a while since I've watched this one and I'm not a familiar with the play as I am with some of the others, but I remember really liking this. Set in a fascist England, the WWII-ish setting worked well.

Romeo & Juliet (Zeffirelli) - Perfectly fine version that I'd have no hesitation recommending.

Romeo + Juliet (Luhrmann) - I do like it, being fairly recent, it's very accessible. The first meeting of Romeo and Juliet and the balcony scenes are visually arresting. Contray to your belief, it does use Shakespearean dialogue.

Rosencrantz and Guildenstern Are Dead (Stoppard) - I know this isn't at all what you're looking for, but if you love Hamlet, this is hilarious. That said, I wouldn't recommend it unless you're very familiar with Hamlet.

Scotland, PA. (Morrissette) - Inspired adaptation. Somehow makes me not hate Andy Dick.

Throne of Blood (Kurosawa's Macbeth) - Great adaptation.

Titus (Taymor/Hopkins) - A visual treat.

Twelfth Night (Nunn/Bonham Carter/Kingley) - Awful adaptation, poor acting, and uninspired production. I would not recommend it. Really disappointing since I love Bonham Carter, I blame Nunn.

On a different but related note, there are a lot of enjoyable comedy performances related to Shakespeare's work, like the Reduced Shakespeare Company. It's just a fun, lighthearted take.