It depends on the game for me, a singleplayer has to be really good if it has to keep me hooked until the end.
I didn't complete Fallout 3, because at some point, it just started to feel stale.
I didn't complete Heavenly Sword because the end boss is a bitch, and I couldn't be bothered.
I haven't completed Dragon Age: Origins, and although it's a good game, I want to have many hours I can dedicate to RPGs like that at a time, and I rarely have that anymore.
I didn't complete Red Faction: Guerilla, because the singleplayer got stale. I felt like I had seen all the game had to offer, and I hope they make the new one more varied, because I love the tech and what they're accomplishing with it.
I haven't completed PixelJunk Shooter because it doesn't feel all that enticing.
I haven't completed Braid, because I got stuck and I want to complete every puzzle as I go along (yup, this thing can keep me from completing a game. It happened with Bioshock and almost happened with Trine. I will finish Braid though. 
)
It's on a game by game basis really, but I hate it when I get the feeling in a game that I've seen everything the game has to offer, and everything from here on out will be variations on this. Red Dead Redemption is a great game, but I'm having a really hard time getting back into it and finishing it because of this.
