Games like Counter Strike, Unreal Tournament, Quake, etc. (the competitive ones) require the use of a mouse if you are serious at all. You need the quick precision and turn-around that the mouse provides, the controller does not provide this.
However games like Crysis, Call of Duty, Fallout 3 and all third-person shooters (imo) work great with a controller. You are allowed to relax and sit back to play these games. Call of Duty 4 does not require you to turn around too quickly too often or to move around too fast. The controller is much more comfortable to hold for long periods of time rather than the WASD and mouse combination. I find my left hand getting cramped from moving around too much and have to sit out after long matches.