Throughout the original trilogy, Jack is joined by star-crossed lovers Will Turner and Elizabeth Swann. He knows they're in love, but just can't seem to keep his eye off of Elizabeth, hitting on her every chance he gets. He does it the first time they meet (after saving her life, then taking her hostage), and then countless times thereafter.
"Elizabeth! You know, these clothes do not flatter you at all, it should be a dress or nothing. I happen to have no dress in my cabin."
Putting the move on Elizabeth is eventually what gets Jack killed at the end of Dead Man's Chest. She approaches him on the deck of the Black Pearl, and the two have an extended kiss that ends with Elizabeth chaining him to the mast, giving her and the rest of the crew time to escape the ship before it (and Jack) are devoured by the Kraken. So, maybe he got what he deserved. Though, this doesn't quite stop him from hitting on her once the third film rolls around:
Elizabeth: "Jack, it would never have worked between us." Jack: "Keep telling yourself that, darling."