Mate, that could range from any number of games available to the world. Hell, there may be people who happen to hate Castlevania, for all I know.
But, if I had to choose a small list of games that I like, which other people seem to hate, the most obvious one would be my most recent game, Sniper. I saw at least one review where the complaints outweighed the praises, yet I absolutely adore this game.
As for the rest of the list, the next obvious choice that comes to mind is, as you said, Mirror's Edge. I believe it had something to do with a perspective issue, where many people couldn't properly gauge when they needed to jump in order to vault a wall, or when they needed to jam the trigger buttons in order to roll and avoid damage or shoot. I know the most annoying thing for me is when I press the disarm button, and instead of disarming the enemy, I instead get beat across the face and shot until I die because Faith failed to react to the command. Aside from that? I couldn't be any less bothered to find out.
Then there was Prototype. This one was actually a flip-around for me. Everybody I knew loved this game and thought it was awesome. I just wanted to get it done and over with so that I could break the disk and remove all traces of ever playing it from my gamerscore. It was fun for a while, but I didn't buy Prototype to play Grand Theft Auto mixed with Assassin's Creed and Mirror's Edge in what I feel is a poorly-mixed combination.
I'm going to finish off this list with Kengo: Legend of the Nine. Being a primarily Japanese game (right down to the language barrier), I can understand where many people wouldn't like it. I imagine many of them only bought it for the sword fighting, and instead of Dante, they got some guy with a ponytail called Musashi Miyamoto, and god only knows how many people actually know who Musashi Miyamoto really is. Other than that? I honestly couldn't tell you why people don't like it.
But, it's all just a matter of preference anyhow; I prefer to play games for the sake of playing and enjoying them, whereas somebody else might here me say this and become brutally sick because I'm not a heavily competitive gamer. Nothing I can do about that, really.