2 words (that shouldnt even go together), Demon's Souls -_- Stupid English

New Game plus I really want to replay a game more often. I love using my max character at the beginning of the game.

huh? if it's not wack and you replay it that's replayability lol, Imo you have to types of replayability the ones were if you replay the game you'll find a bunch of news things: ennemies, loots or whatever (borderlands) or the game is so freaking good you got to replay it (knack or final fantasy 13)

I think it's about multiple playable characters, multiple classes, unlockables, multiple endings, multiplayer modes -- all things that would bring a player back after his or her first playthrough. I don't believe a game's "fun factor" should count toward its replay value. For example, Shadow of the Colosuss, despite its greatness, doesn't have high replay value. Infamous, with its branching morality paths, collectables, and upgrades, does score extra points in that category.

When I am not bored with the game after finishing it

Goldeneye.

If it's fun to play a second time and then subsequent times

Some of my most replayed games are the ones people say they would only rent. For instance I go back once a year to Uncharteds, Ratchet and Clanks, Jaks, Slys, Resistance 3, Heavy Rain, Beyond 2 Souls, Journey, TWD, GoW, MGS games, and many more which are very cinematic and most of which I've platinumed or done everything I'm going to challenge and collection wise. I go back to them because they're a blast to go back to. It's kinda like watching a favorite movie. You're getting the same experience (well in games it always plays out differently and is interactive obviously so that gives it more variety) but you just love the way the story is told (or how the story PLAYS out) and you can't get enough!

I rarely replay games, so its fairly meaningless for me. The actually important term is general "value" which is determined by how long the game is and how much variety the game has (games designed to replay like Star Fox would have the replay time contributing to game length). I would never think about playing Xenoblade again, but my first playthrough was over 100 hours so I consider it to have had plenty of value.

Mario Kart.

This may go against Kowen's definition, but I always get an urge to play MK again and again.

Replayability is the virtue of a game to make me feel compelled to play it again; it doesn't matter if it is because the game granted me some costumes for the main character for beating the game, if it is to experience different endings or just because the game was simply awesome.