JoJo's Bizarre Adventure: JoJolion: In Joshu Higashikata's A Day in the Limelight arc, "Milagro Man", Joshu goes to see a Pirates of the Caribbean movie in theaters (likely On Stranger Tides, since the manga started and takes place in 2011), and buys 9 seats and sits himself in the middle so that he doesn't have to be around noisy moviegoers. After the movie, the theater holds a raffle, and Joshu wins, earning himself a figurine of Jack Sparrow.
Pleasant Goat and Big Big Wolf: The official English YouTube upload of Joys of Seasons episode 42 features the text "Don't be a pirate unless you're Jack Sparrow" in its title.
iCarly: In "iStakeout", Carly and her friends scope out a guy who was reportedly selling pirated movies - it turned out he was actually selling low-budget pirate movies he made with his friends. Anyway, one of these movies is called Pirates of the Lima-Bean.
Sesame Street: A "Cookie's Crumby Pictures" sketch is entitled Cookies of the Carribean. In this sketch, Cookie Monster, as "Captain Snack Sparrow" learns to focus and not give up when trying to reach Davy Jones' cookie jar.
In Aladdin (Virgin Games), the prison scene for Pirates of the Caribbean is recreated in the background of the Sultan's Dungeon, complete with a keyholding dog.
Pirate Hunter has large-scale battles in the final levels lifted directly from Dead Man's Chest and At World's End, with the hunter battling legions and legions of sea-creature-human hybrids with magic weapons.
In Stellaris, one class of Space Pirate ship is the Black Earl - just one letter off the name of another pirate vessel, the Black Pearl.
In The Witcher 3: Wild Hunt at the docks in Novigrad, Geralt can run into a sailor who asks n "Why's there never enough rum?".
Wetbeard from Castle Cats has a line which has him saying "We need to catch that sparrow!", which likely is a reference to Captain Jack Sparrow.
Admiral Swiggins from Awesomenauts had community-chosen voice lines, which naturally gave him a few Shout-Out voicelines. One of them being: "Do you fear death?".
A possible scroll on the bottom of a Picus news broadcast from Deus Ex: Human Revolution is, "Pirates sighted off the coast of Tortuga".
Futurama: In "The Series Has Landed", one of the attractions at Lunar Park is Whalers of the Moon, starring a gang of musical animatronic sailors, one of whom recognizes Bender.
Bender: Aw, geez, I went to high school with that guy.