Play Skies of Arcadia dammit! It is a JRPG about pirates and it has Vyse and company.
Shantae: the first Shantae game is available on 3DS eShop. My first impression of it was highly positive, but it mellowed over time. The scope of the game was smaller than I expected and it's...extremely straightforward with the exception of the squid collecting; nevertheless, it's a pretty impressive title for its time. I contributed to the Kickstarter for the new Shantae game and will be playing it. The concept of piracy is on the periphery more than anything. The main villain is a pirate and she is a mean person who has a pirate ship that she uses to attack stuff.
Mega Man Legends: the concept of piracy is also sort of secondary here. You frequently encounter the Bonne Family within the two main games and they do attempt to terrorize or do otherwise bad things, but the games generally treat them as comic relief instead of any sort of real threat. Being air pirates and with all of the technology present there isnt much that's analogous to the "classic" romantic notion of pirates but they are pretty fun games, though the combat is clunky in hindsight.
Monkey Island: Having only played the first game, the classic pirate sensibilities and aesthetic are much more at play here. It's supposed to be a humorous game but its absurdity might not appeal to all, though I liked it. It's not a mature game but it's really quite adult. The puzzles are obtuse and intimidating for some - more challenging than what you might expect out of Phoenix Wright and certainly a lot less guided than that franchise; I actually needed help for that grog transportation one, and I make a point of not doing such things! Anyway, this game feels very old school, but I certainly recommend it. I played it through a remake put on XBLA - if its still there, buy it!