I know I'm pretty much alone in this but I really don't need anything other than for the game to be good/fun. I don't stop playing game just because I finished it once. I will play it again and again, depending on the length of the game I might play it often or I might take breaks between but I will definitely keep it and play it again at some point.
I've always hated the traditional concepts of "replay" value because it's always based on "oh well this game has x amount of extras" or "multiple endings!", etc. Don't get me wrong, I like that stuff, those are cool extras to have and can add to a great game but personally those things aren't what makes me replay a game.
The only thing I can think to compare it to is like a good movie or song: Sure you've seen the movie and know how it ends or you've listened to the song and know the lyrics to it but you still want to watch it or listen to it because it's good and you like it.
That's my philosophy with games. If I like the story, the characters, and/or the game play is really fun I'll keep coming back because I enjoy it but that might be because gaming is at the center of my hobbies and is my main form of recreation in my spare time (probably why I can't finish my own game, LOL). I mean I still have and play games on my Atari, NES, SNES, N64, Gamecube, Wii, Xbox, PS1, and PS2. And that's just my old gen systems.
Anyway, my long winded post aside, my answer is: If the game is fun, I don't need anything but the main game to bring back for another round.