If I don't finish a game on a play-through, but then feel like coming back to it a long time later, I usually end up restarting it. And there are many games I've played and "died" (often numerous times) or just gave up that I never won.

As for games that I've started, and stopped in the middle, but still had saves that I went back to to advance the story to the very end:

StarCraft took me about 5 years from start to finish--not because I don't love the game, but because there's only so much RTS I can stand in a day or a week.

LoZ: Windwaker took me 2 years...I obsess over getting every item in those games and I got tired of all the boring sailing to find them all.

Command & Conquer Generals around 3 years. There's a level in the Chinese Campaign that I just didn't have the right mind to develop a strategy to beat...it's the one where your nuke cannons are ambushed by mobile bio-scuds in the opening cutscene. I couldn't for the life of me figure out a way to stop the GLA from eventually over-running my base before I could vaporize their's. After someone told me the solution, I finished that Campaign and the American Campaign rather easily, but then got stuck on a level of the GLA Campaign that took me about eight months of playing off and on to figure out.

Pokemon Red/Blue/Yellow/Gold/Silver/Crystal around 5 years. Again, an obsession regarding collecting, in this case high-quality versions of every Pokemon in the game ('cept for Mew). And because of the brilliance of Nintendo, they got me to play the same two games three times each, which in part accounts for the time it took me.