This is one of those fuzzy, non answers I'll always give to this sort of question: It depends on the game. Seems obvious but there you go. Playing Heavy rain a second time was pure torture, even though I enjoyed it well enough first time round (gaping plot holes aside). Whereas I could easily replay F-zero Gx tomorrow, or hell, even Wind waker, which I've finished around 7 times already (Ocarina and Majora's mask are in double digits). Goldeneye, Perfect Dark and Timesplitters have also had plenty of replayability for me.
A replayable game needs a few criteria: Gameplay is first and foremost. Story based games are infinitely less replayable. Though a great atmosphere can also add a lot to replayability (see: Zelda). Genre type is also important. Racers, fighters and sim games are hugely replayable. Shooters moderately so. Puzzle games, such as Portal, are really limited in replayability.
Lastly, pacing. I said I like replaying Wind waker, but I nearly always stop after a certain point. And if you've played the game, you'll know what point. A games pacing flaws become magnified times a hundred on repeat runs, and bits where it's boring become more intolerable, since you don't have the drive of looking forward to what comes next. The game must be enjoyable without that drive, which is a rare enough thing to do. In films, anticipation of what's the come isn't just a cheap ploy to keep you interested, it's a core principle of movie making, an inherently good thing. What keeps things driving on the first run can leave it dead on the second and beyond. Games can circumvent this by pure mechanical enjoyment, hence why Multiplayer is so popular: Solid mechanics, with a layer of unpredictability to hone said mechanics, with varying degrees of sociability to spice that up too.