A few things come to mind:
If the game is an RPG or open-world of some sort, basically any type of game that contains side-quests and missions, the only way I'll be interested in actually doing them is if they actually feel connected to the story or the general tone of the rest of the game. If they just feel like they're there for the hell of it, then I won't be interested in it.
If a game has a long story and suffers from repetitive gameplay, I'll generally get bored of it about 25%-50% of the way through, unless the characters and aesthetics are really astounding. Hell, sometimes even if the game is short, repetitive gameplay will just turn me right off before I finish it.
Also, games always seem to know when it's been a few hours since I last saved, because they always crash or give me an enemy that I can't possibly defeat, so that I lose all of the progress that I made.