Dead Premonition. In all fairness, a lot of the reviews were accurate. This game is clunky, it feels like an unreleased Dreamcast title, and it's too absurd to take seriously at all. But to me that was the charm. Easily one of the most hilariously insane games I've ever picked up. If you have 20 bucks, an Xbox, and are able to "get" the so-bad-its-good thing, then I suggest picking it up and giving it a try.
Deadly Preminition is a very refreshing game to play in between the RPGs that I usually play.
In terms of games that were critically mauled that I enjoyed, I always think of the Resident Evil Outbreak games. I was well aware of their shortcomings; repetition and slow gameplay, but I still really loved them. I've given up hope that there will ever be a File #3, though, just like I've given up on there ever being a sequel/spiritual successor to Silent Hill 2. :(