Regarding movies, if you're a purist, you can see all the plays performed in their entirety thanks to the BBC's television series where, over a series of years, they filmed every one of his plays without making any cuts or changes. Unfortunately, purchasing all of them is quite pricey, but you can get them from your local library, even if you have to request inter-library loan. Lucky for me, I could request the university to purchase them as a teaching supplement.
While the BBC productions have terrific acting and are true to the text, they also have limitations; certainly, the budget is much smaller than that of a film, and it shows. Secondly, some of Shakespeare's work simply does not translate well to the small screen. It can seem overlong when you're watching it on a television rather than a stage.
I enjoy film adaptions that keep most of the play intact and choose their cuts with care, but I understand why the cuts are necessary and don't begrudge them. I only begrudge them when they change too much and the play loses its punch.
Also, despite the fact that the original productions in the Globe had a minimal set, I like cinematographers to take advantages of the medium's larger scope to give the locales and sets additional realism.
A pet peeve of mine is when they change time periods. It takes the plays out of context. A lot of times it's done to make a "statement" - like the modernized Macbeth starring Patrick Stewart which likens his character to the Communist revolutionaries of the early 20th century - or to make it more "accessible" such as that awful modernization of Romeo and Juliet in the nineties starring Leonardo DiCaprio and Clare Danes. Sometimes it's done for no apparent reason at all, which is even worse! That's why I can't get behind Branagh's Hamlet, as much as I love his other Shakespearean productions. Moving the play up a few hundred years was so gratuitous that I wonder if he did it simply because he thought 19th century costumes looked better on him.
While the BBC productions are the truest to the plays, here are some film versions that, while not entirely true to the plays, I find entertaining (you'll note two directors who are excellent with Shakespeare that keep popping up, lol):
Branagh's Much Ado About Nothing
Branagh's Henry V
Parker's Othello
Zeffirelli's Romeo and Juliet
Zeffirelli's Taming of the Shrew
Zeffirelli's Hamlet (controversial, I know, but I think it works for all its flaws)
Olivier's Richard III
Radford's The Merchant of Venice
Brook's King Lear (the 1971 version)
Also, in spite of the swath of cuts made and the extremely low budget since they were produced for 1960s television, I love An Age of King's presentations of Richard II, Henry IV (all parts), Henry V, Henry VI (all parts), and Richard III all in a line using the same actors - including a young Sean Connery as Hotspur!
For the rest of Shakespeare's plays, I haven't yet found movies that have struck me as particularly well-done, except the BBC productions of course.