I finish most of my games (storywise and in RPG's also most or all side quests), there are a few exceptions if the game was really horrendous and not worth completing.
But if you count in all these damn achievements you have to get nowadays then I don't finish a lot of games.
It is just a chore to extend games, the requirements for some achievements are often ridiculous and if I would do them I know I would hate the game afterwards, so I just don't do them and I can play it again if I want to.
edit:
kman123 said:
I either don't finish games due to extreme boredom (Dragon Age), a lack of interest in plot (Dragon Age) or because of unnecessarily bullshit gameplay (Drag- ok, Nier.)
Hey, don't hate on Nier
If you got past the first hours and completed the endings the story is really nice, the only thing I hated was the fishing as I never got the fishs I needed.