Call of Duty 4, lately I have been using a sub machine gun with a silencer, and a radar jammer along with smoke grenades. If you know what you're doing you can rack up a lot of kills without getting killed much yourself.
But it is still basically a teamplay shooter...
Freeware: Warsow or Nexuiz... Not that good in the graphics department but kinda fun to play IMHO and popular. I say that from a once avid Q2 gamer's perspective.
By the way - you brought up an interesting point here. I just noticed that there are indeed VERY FEW non-teamplay online shooters coming out... It may very well be that co-op shooters are better at creating communities and players drawing each other into the game but I see a major unoccupied niche here (at least nowadays)...