Diddy Kong Racing. I've had it for about 11 years now, and I still haven't beaten it. I am currently going back and beating it as I speak, but I've yet to do so. Nor did I ever beat Kirby: The Crystal Shards.
Come to think of it, there's not many games that I HAVE beaten. If you take out the ones that I beat with a guide or cheats, then I've only beaten Viewtiful Joe 2, Tony Hawk's Underground 1, 2, and Wasteland, Rayman Raving Rabbids, Mario Galaxy, each Smash Bros, and Metroid Fusion. As a gamer for 11 years, this is a staggeringly low completion rate.