carnival73: Age of Pirates is the most definitive of the series but the early games provided no over head story or ending so you just sailed around forever pointlessly.
City of Abandoned Ships kicked the franchise up a notch by finally including a story and something to build towards:
http://www.gamersgate.co.uk/DD-AOP2CAS/age-of-pirates-2-city-of-abandoned-ships GG takes this game down and puts it up again, from time to time, and used to have a copy on their US site (guess they can't make up their minds).
Note the game is quite clunky and poorly polished but it features everything you would want in a Skyrim-Like Pirate game and more!
Pretty much this. Its also known as Sea Dogs 2. Its very open ended, and with fan modifications, you get a complete overhaul that fixes most of the bugs. The game itself is not very intuitive however, and it takes a bit to learn the things you need to know, but once you do, oh man, you have a huge world to explore. Great game!