I only finish the games that keep me interested, that's fun, that isn't a chore play, that have no glaringly obvious cock ups in engine/movement/aim (ie. many ported titles), and dare I say it, what actually works on my hardware, LOL. If it's super resource heavy, I leave it for later, when I can experience it's full omg-wtf-that-looking-ama-zing.
Replay value also spurs me on to finish a game. If I see, that I loaded a previous area/stage/section/map, and the outcome is different, or the game allows me to make different decisions, to complete an object, that not only makes me want to replay the title, but while I'm playing for the first time, it'll push me to finish it that much quicker. Examples would be FEAR, Farcry and Crysis series. Better AI or sandbox maps/stages, are win (obviously I mean the ones that work well, not the I-can-do-anything, including work myself into a position, where I can't continue type of sandbox)
Oh yes, and number one reason, I don't finish a game is, something way cooler, rocked up...