The best pirate themed board game I ever played is Blackbeard by Avalon Hill.
I'm not sure if it's easily available anymore but it's a great pirate game. It's a little more historical sim (GMT after all) than game, but could be quite good if you have 4-5 that are really into it, but not as great solo (that is why I didn't bite).
And if I recall it can actually be played solo as well.
Black Fleet (2014) by Sebastian Bleasdale.
- Mechanics: Area Movement, Pick-up and Deliver, Variable Player Powers
- Average rating is 7.1125; rated by 2802 people. Weight: 1.9608
- Board Game Rank: 578, Family Game Rank: 101
Port Royal : push your luck card game with pirate theme.
It's easy to explain, with quick turns and expansion which adds contracts cards as additional things to compete for (that even makes game playable solo or cooperatively), without adding complexity.
Its designed by (Alexander Pfister: Mombasa, Broom Service, Isle of Skye, Great Western Trail).
Another big plus for this game is that it has active participation for all players during every turn.
Highly recommended (both the base game and the expansion)