I typically try to finish any game I start, however I can really easily jump ship from a game I am somewhat enjoying to something else I have been anticipating once it gets released. That other game may then sit on the shelf for months or even longer before getting played again (if it gets played again at all). I've been trying to do better with this, since I have such a backlog of unfinished games, but this does mean that now if I am not enjoying a game, I don't bother trying to finish it and move on to something I do enjoy.
For instance, I continually get bored with Bioshock any time I try to play it. I've started the game three times now, but always stop playing after a number of hours. It just won't grab me for some reason. Similarly, the games Chronovolt and Rayman Origins for the Vita, which were PS+ freebies, bored me within minutes, so I put them away. I tried to give Lone Survivor a chance, playing through a few hours total, but it just didn't do anything for me either. Maybe if I ever get through my backlog I will go back and try these yet again, but with various upcoming games, I don't see that happening anytime soon.