The Last of Us
As evident by my sister playing this game more than 5 times on the same difficulty (will never understand why she didn't up the level, but okay...), this game was beyond good enough to warrant multiple replays on single-player mode. The game mechanics were interactive enough to make me want to keep playing, and even though it does eventually end, the challenge of upping the difficulty makes you want to replay the game.
Crisis Core: Final Fantasy VII
One of my favourite games, and I'm not adding it to my list because of that reason. More so because the story was well-done, and it would make me want to replay the game multiple times, regardless of whether it's basically going through the same events over, and over. A game as good as this one deserves replays.
Bravely Default
Haven't beaten this game myself, to be quite honest, but the mechanics of this game are particularly interesting even though they are rather similar to traditional turn-based RPGs. Nevertheless, the cute animations, comedic lines within the story, and the loveable characters make it to my list!
Katamari Forever
Or any game from the Katamari series for that matter. All you do is roll objects up, making the ball as large as possible. What more do you need? I particularly liked Katamari Forever more than other instalments because you have the presence of cousins, and presents that act as collectibles that you can obtain throughout the game. Not only that, but there are endless modes that can be unlocked for the levels.
Final Fantasy XIV: A Realm Reborn
Have to have at least one MMO on the list because they can be endless, in theory. Granted that you're allowed to interact with people in games even though you're on a deserted island, this would be a nice reminder that there is still civilization elsewhere XD
As for the rest, I think I'd have to include: Tales of Xillia, The Legend of Zelda: Ocarina of Time, Chrono Cross, Final Fantasy VIII, and Theathrhythm Final Fantasy.