As already recommended by Captain Blood, appropriately enough,
The Sea Hawk - a swashbuckler directed by Michael Curtiz and starring Errol Flynn (along with Olivia de Havilland and Claude Raines - they'd all go on to make the definitive
Adventures of Robin Hood and most of them would also make the film
Captain Blood). Dame Flora Robson plays Queen Elizabeth.
Flynn reappeared in
Elizabeth and Essex, with Bette Davis in the other title role.
Shekhar Kapur's two
Elizabeth films, also on the Captain's list, are visually gorgeous and blessed with terrific performances from Cate Blanchett. The first is a strong personal story, the second more of a jingoistic pageant. As with pretty much everything on celluloid or digital video, don't trust them as history.
The 1970s version of
The Prince and the Pauper is a little early (being set around the accession of Edward VI), and nearly sunk by the almost unbelievably bad performance of Mark Lester as the look-alikes, but it was written by George Macdonald Fraser and directed by Richard Fleischer with something of the fizz, humour and energy of the
Three Musketeers films (also written by Fraser) which were their obvious model; Oliver Reed is tremendous as the drunken hero; there's a cast list to boggle at (Charlton Heston, Ernest Borgnine, Rex Harrison, Raquel Welch, David Hemmings, George C Scott ...) and Lalla Ward is splendidly haughty as the Lady Elizabeth.
You'd think that anglophone cinema would have made films about Drake and Raleigh, but I can't think of any specifically. There was a TV series called
The Adventures of Sir Francis Drake in the 1950s, but I haven't seen it. It was an adventure series in the mould of the successful
Robin Hood. Glenda Jackson's performance in the TV series
Elizabeth R is legendary, but I admit that I haven't seen that either. She reprised the role in
Mary, Queen of Scots, opposite Vanessa Redgrave as Mary. Jimmy McGovern (creator of
Cracker among other things) wrote a striking pair of TV dramas about Mary and her son, James VI and I, called
Gunpowder, Treason and Plot.
Stretching the period a little into James's English reign also gives us Terence Malick's
The New World, based on the story of Captain John Smith and Pocahontas. There's also Disney's animated
Pocahontas, of course.
For the French religious wars, there's the bloody and brilliant
La Reine Margot, with Isabelle Adjani, from the Dumas novel about the incident that gave us the word "massacre". Shamefully, I am ignorant of other films of the period in other languages.
Then there's Shakespeare. The 1970s-1980s BBC productions, available in a DVD boxed set as
The Complete Dramatic Works of William Shakespeare, generally have more Elizabethan (or Jacobean)-flavoured productions than the movies. For what they might actually have looked like when performed at the time, see the opening scenes of Olivier's version of
Henry V. The reconstructed Globe Theatre has also released videos of some of its productions.
Shakespeare in Love is an absolute hoot.
As for productions of other playwrights of the period, I'm drawing almost a blank. There's a film of Marlowe's
Doctor Faustus with Richard Burton in the lead and Elizabeth Taylor silent as Helen of Troy, but it's a bit of an oddity - it was made as a fundraiser for the Oxford Playhouse, and all the other roles are taken by members of the Oxford University Dramatic Society. Alex Cox's version of Middleton's
Revenger's Tragedy is set in one of those clichéd but cheap post-industrial wastelands the director is so fond of. Surely there must be some spanish-language films based on the plays of Lope de Vega?
Finally, Google threw up this list, which might be useful.
http://en.wikipedia.org/wiki/Category:Films_set_in_the_16th_century