Sid Meier's Pirates!
Just to get a couple things out of the way: First of all, yes, ARRRRR, fine, okay. And second, yes, Sid Meier's Pirates! is a port of a 2004 PC game which is itself a remake of a title which made its Commodore 64 debut in the Gameozoic Era, way back in 1987. It must be noted, however, that the first version was considered a classic of its time, and this edition, while not by any means spectacular and revolutionary, is as much fun a gaming experience as you're likely to have.
The story involves the player, as a young European of some type, being cast out into the wide world of the 17th century after his family is betrayed and his fortune stolen by evil nobility. Taking up the Jolly Roger, Captain Player vows to swashbuckle his way across the Caribbean to steal back what's his. This is done through lots of varied and mostly well-done gameplay, including ship-to-ship shooter battles, a simple but challenging timing-based fighting game that features swordplay in boarding actions and duels, some fairly lousy dancing, a turn-based strategy-grid for large land actions, such as ransacking towns, and even a rudimentary trading structure. As far as role-playing goes, you can ally with any of four nations, or none; captain a fleet of many different ship types; get married once, lots, or not at all; and be as valiant or dastardly a sea-rogue as you want before the game ages you 'til you're too old to pirate anymore.