This may be cheating, but both my little brother and I have a PS3, and he (for some completely inexplicable reason) got Duke Nukem Forever for his. I've played through all of his other games, but I have absolutely no interest in touching that. From what I heard about it, playing it would be like voluntarily subjecting myself to some kind of bizarre torture. Never gonna play it.
As for a game that I own, I suppose I would say both Little Deviants on the PS Vita, and Final Fantasy VIII as a PSOne classic. Deviants came in the First Edition Bundle with my Vita, and while I initially intended to at least give it a try, reviews dubbing it as 'shovelware' kept from doing so. I got enough of shovelware games on my friend's Wii. We were so desperate to play anything on that thing...
As for FFVIII I downloaded it back in the summer, when I really wanted to get some use out of my Vita. I actually started playing it, but the cast of characters is so completely unlikable that I have no intention of finishing it. Which is odd, because I liked Squall just fine in the Kingdom Hearts games (where he was christened 'Leon'). I guess it's just who he's paired up with. The voice-acting probably helped a bit, too. Whenever I read his dialogue, I always made it sound like a huffy teenager. Can't be bothered to finish it when I have absolutely no interest in what happens to the characters.