I have made a point of collecting and watching all pirate and historical seafaring films and TV shows that I can find. I'm still missing out on some, but one day....
While I do have that version of Treasure Island; it is on my to-do list to actually watch.
Also trying to get myself to watch the recent TV series of Crossbones. Saw the first two episodes,
but I found the absolutely ridiculous look of the chronometer to be really very annoying.
Black Sails is interesting, but there is too much talking and not enough honest pirating for my liking.
And everyone seems to be betraying everyone so that in the end basically nothing happens. Oops.
Haven't yet watched all the recent episodes, but I sincerely hope the Jack Rackham character will end up using his REAL historical flag.
He made a big deal about wanting his flag to look right and since his flag is one of the most famous ones ever,
if they are going to make a point about his flag, they might as well make the RIGHT point.
Blackbeard's flag in PotC 4 was quite embarassing because it looked nothing like his real one.
Of course they had already given his real flag to another semi-random pirate in the third film, which probably explains why they had to come up with something else.
Still stupid though.
Anyway, my favourites are:
Old black-and-white version of Peter Blood with Errol Flynn: The other Errol Flynn ones are also fun, though a bit less so as far as I'm concerned
1962 version of Mutiny on the Bounty (though the older one and newer "Bounty" are good as well)
Old film of Captain Horatio Hornblower, R.N.: Not pirating, but SOOO good
The Crimson Pirate: A bit of a comedy and not realistic whatsoever, but lots of crazy piratey fun
Hornblower TV Series
Cutthroat Island: I don't care what "everyone" says. It is proper pirating, probably the most "everything a pirate film should have" one ever. Plus the music is far beyond amazing.

Pirates of the Caribbean: Entire series, but especially the first film
Curious ones:
Yellowbeard: Monty Python style crazy stuff
Swashbuckler: Made well after the end of general pirate films
Nate & Hayes (Savage Islands): Not so old film with Tommy Lee Jones, with cannibals, Germans and an armored steamship