"Tomb Raider" for Sega Saturn because I really hate Tomb Raider, though I'm proud that I actually own the more rare Saturn version of it.
It was actually free without the seller knowing. It was at a flea market and I had just bought my first Sega Saturn so the man threw in a game with it for someone finally taking it off his hands. I chose Sonic 3D Blast and inside were that and a copy of Tomb Raider under it. Since Sega used those gigantic jewel cases back then for Sega CD and Saturn games, there was no real way of knowing since they all some weight to them.
Another of my shameful games is simply called "Dance Aerobics" for the 8-bit NES. It required the Power Pad (which I also have) to play. The tag line on the cartridge label reads "Hop, skip and jump your way into shape!" Ironic when I think about the existence of Wii Fit since this aerobics title was also made by Nintendo.
Lastly, I'm ashamed to say that I own one of the thousands of cannon fodder copies of "Doom" for Sega 32X. It's shameful because it's such a horrible conversion of the PC classic. It's missing levels, the screen is cropped and when you beat it, it crashes to a green screen with a C:\ prompt. No one has ever been entirely sure if that was a glitch or on purpose. It's both funny and sad at the same time.