Half-Life really isn't that generic. I mean, in concept, maybe (because we totally haven't seen all hell breaking loose in research labs before), but the gameplay is quite unique (a whole bunch of stages that nearly seamlessly flow into each other, giving the appearance of one large world instead of Level 1, Level 2, etc; plot details being given to you in the middle of the stages; large emphasis on teams of enemies working together to take you down, instead of teams of enemies mindlessly running at you as if they were doing it solo; and so on and so forth).
Plus, the hero wasn't just a generic, white, macho military grunt - granted, he's still white, but he was a meek, nerdy scientist, with the only thing separating him from the other meek nerdy scientists being the HEV suit he had to wear as part of the experiment. He hadn't really done much with firearms before, IIRC (although given his proficiency in using all of them as the game goes on, could've fooled me).
And, as has been said before, Team Fortress 2. One of the few games that doesn't focus entirely on killing the other team (just mostly on it). Unique setting, unique art style, extremely unique gameplay. Enough said.