If you are looking for a good pirate-themed game, take a look at Pirates of the Caribbean (2003).
It was supposed to be Seadogs 2 but Disney bought it and changed the title. Don't worry about Disney goofiness, the only link between the game and the title is a legendary ship named the Black Pearl and that's all. The rest is what you expect from a pirate game that's not trying too hard with the swearing.
https://www.youtube.com/watch?v=2g12XAOMdQw
It aged very well because what was beautiful back then wasn't related to horse-power: the setting sun on the water, the architecture, the lush jungles, etc... it's still a wonder to look at.
Its most serious flaw would be its floaty combat on foot. You better be ready to invest in guns so you can block and just one-shot people with your pistol. The boat-to-boat combat, on the other hand, is delightful, and hits the exact right spot between arcade and believability.
Its other major issue is level-scaling (in a game edited by Bethesda? Colour me impressed): I was fond of the early game fights, with small-to-medium boats and limited scale, with the occasional heroic assault on a big galleon with your tiny sloops buzzing around it like little bees. Sadly, towards mid-game, just about every convoy you meet is not one, but several huge galleons and you need to have the same firepower if you are to do anything. All diversity disappears.
It's one of these open-ended games that may lack polish in some areas, but really give you a sense of wanderlust and exploration, because it lets you do things that have no purpose other than "feeling" the game (call it the dreaded "immershun"): switching to in-world mode in the middle of nowhere just to look at your ship sailing in the dawn, or close enough to the coast that you can dock in real-time, a process short enough not to become a bore, but long and deliberate enough that you can capture the instant. And of course you have all sorts of pirates' villages, colonial cities with typical architecture, great costumes, etc.
One last point on the interface: it's a console port and it shows. Thankfully, you don't access the non-action interface often enough that it prevents you from playing, but a USB controller with Xpadder will probably make the experience much smoother.
