Short, replayable single-player.
But that's not the whole truth :P
I love games that are quite short but challenging. Coming back to lengthy games never works for me so I need to sit down and have a shot at finishing it within 3 days max. Otherwise it won't be an awesome game to me, just "good".
I love it even more when those short games make me have to try dozens of times to finish them or go for highscores/time attacks that demand precision and memorization of small, fast movements.
Sounds a lot like arcade games, right?
On the other hand, I love games that are like Mario. "Mission" based and not story driven. That way it's always easy to dive into it.
But I'm also into couch co-op and will buy games just because they offer this.