Strangely enough, the Yakuza series features this heavily, especially the latest one, Like a Dragon.

Every game has a separate "Completion Log" which gives you a bunch of different tasks to do, which ranges from performing certain actions in combat, eating every item in every restaurant, getting the high scores on various arcade games, minigames, etc.

To give you an idea of how addictive this can be, I beat Yakuza: Like a Dragon's main story at 65 hours or so, but didn't finish the completion log until 140 hours.