What triggers you to play through games twice?

Nostalgia 

Definately new game +. I love going through a game again with the stuff I already collected. It's even better when you can start a new game + on a higher difficulty. Another obvious reason is if there are no games out that I want to play more. Usually I only replay immediately after I finished it, I don't come back to it months later. Lastly games with different classes (RPG's) with distinct playstyles where I want to try a couple, usually don't finish those playthroughs though just want to sample it.

Achievements

boredom is part of it.

sometimes i just wanna play through something again because it was fun or because the story is interesting and good enough to see again. sorta like watching a movie again. or watching a rerun on tv, just because you've seen it doesnt mean you cant enjoy it again. same thing with games.

i have books ive read 3 or 4 times. i have movies ive seen a ton of times, i have games ive played through a ton of times. i see it as all the same thing really. entertainment you can enjoy more than once.

i usually don't replay games. i just beat them and leave them. i am thinking about replaying mass effect 2 again. the game was pretty cool game.

It's very rare I don't complete a game at least three times, once on normal, then hard then back to easy for a laugh. Other than that, as long the gameplay is entertaining I'll continue to play it. 

I'll usually only replay games if they're on the short side (anywhere up to ten hours in length), and for achievements if they're recent games. I usually never replay longer games such as RPGs,n unless there is a large amount of character customization and possible deviation in the quests.

I only tend to replay things that are mechanically pleasing. That is, games that derive their appeal from the actual act of controlling the on screen action (as opposed to story, atmosphere, etc.) Bayonnetta is the best example that I can think of, but a lot of FPS and puzzle games fall into that category as well. Also, I usually only replay games with level select options. If I finish something like Fallout 3, it just feels like it's too much to take on a second time. If I can go back and play through whatever part I happen to be in the mood for at the time, though, I'm much more likely to revisit the whole thing again.

When you think a game is exceptionally awesome, chances are you'll want to play it more than once.