I think my standards are quite reasonable, for whenever I buy a game, it must do one or more of the following things well:
Visuals: Not "graphics," but what the graphics show. For example, Okami is entirely cel-shaded (save for the neat painting-scroll things that introduce new enemies), which to my understanding is fairly old and not particularly demanding of the developers or the hardware. But it is a beautiful game, you cannot deny. I'm also one of the twelve or so people who bought Fragile Dreams: Farewell Ruins of the Moon. It's an action RPG with absolutely horrible controls, but it paints one of the most haunting and original tales of survival in a post-apocalypse I've ever seen. Ehh, I'm still an idiot for buying it for $50, but I couldn't find a deal on it anywhere, so I finally gave in.
Gameplay: I'll buy a game if it's fun to play, generally. Prototype has a generic city-scape as its backdrop, so save for the cool designs on the main protagonist's mutant powers the visuals are nothing special. The narrative is a bit silly as well, with your standard "big corporate conspiracy" mixed with "zombie apocalypse," not to mention the disconnect between the protagonist's portrayal as a sympathetic character, despite having been granted super powers and murdering hundreds of innocents every mission. Regardless, Prototype is a blast to play. It's fun to run up buildings and leap hundreds of yards in the air, and there's trainloads of tanks, soldiers, zombies, and screaming civilians to fight.
Narrative: Games that tell a great story or display superb artistry get my attention as well. I was not impressed by the generic sci-fi visuals of Mass Effect, nor was the gameplay that great, with its baroque RPG elements or bland third-person-shooter elements. However, when it comes to storytelling, it's one of the best. Good ol' BioWare made sure of that.
Ideally, I want a game that does all three well, like Bayonetta or No More Heroes, but the better a game does in one area, the more forgivable its other areas are.