Up until a couple of years ago I did not finish most of the games I played, so it was common for my favorites to be unfinished.
I've recently gotten a lot better about seeing them through to the end, but looking back it was probably Metal Gear Solid V, I remember thinking it was one of the best games I'd ever played, yet I never got around to finishing it (and I know for a lot of people the later chapters ruined it, so maybe if I go back I'd change my tune).
Also, Fantasia: Music Evolved. Absolutely one of the coolest games to come out last gen, but I tend to just get on freeplay instead of continuing the story, and now that the newer Xboxes don't support Kinect it's much more of a hassle to set it up.