We've already got lists for movies and books, so let's move onto some great pirate-themed video games. Hopefully we can connect gaming fans here to games they may not be aware of.
Assassin's Creed IV: Black Flag (2013-Multiple consoles) - The newest title on this list. Most people in the gaming world know the AC series, and ACIV is one of the best regarded in the series. The game takes place in 1715 Caribbean, and while the game takes plenty of liberties with history, it still tells a great story. It's also got fantastic gameplay and has a very well-known open world that allows for tons of exploration.
Sid Meier's Pirates! (2004-Multiple consoles) - I'm mostly referring to the 2004 remake, but I know the original '80s game has plenty of fans as well. This game is probably the closest to how a game of 7th Sea might go. You even choose one of several real-world nations to sail with initially. The game is extremely free-form, with little in the way of structured plot. That go-your-own-way style tends to be the determining factor to whether a person likes the game or not.
Skies of Arcadia Legends (2002-Gamecube and Dreamcast) - This game is criminally underrated in my book and commonly appears on lists for best games that never get a sequel. This Japanese RPG has many tropes - fantastical setting, plucky teenage hero, cartoonishy evil empire - but the plot's a lot of fun and the skyfaring world is great to explore. The Dreamcast edition had some mechanical clunks, but the Gamecube version fixed them and added even more content.
The Secret of Monkey Island (Multiple Consoles) - The Monkey Island series has had many sequels, but the original will always be the best in my heart. It's playable even in its original 1990 PC incarnation, although it's been remade several times since. Hysterically funny and with great visuals and puzzles, The Secret of Monkey Island helped define the point-and-click adventure genre and stands as a classic in early PC gaming.
Thoughts? Other recommendations?