Since I'm certain that I pwned more in Counter-Strike at 200+ FPS than at 100 (back then it was on a 100Hz monitor), I wrote a little explanation of why (I think) this is, for myself and for people like skeeter... :p
Crudely speaking, there are delays between the last polled mouse position, the last frame rendered by your GPU, and the last frame displayed by your monitor, and these delays impact how up-to-date the stuff you see on your screen really is.
Your monitor will display whatever your GPU last rendered at a fairly constant rate ("refresh rate"). Your GPU renders new frames as fast as it can, but generally not at a constant rate, especially if the scene it renders is sophisticated and ever-changing, as is the case in computer games. In a first person shooter, what exactly your GPU renders depends on your mouse's position, and mouse position updates aren't instant either – they too have a delay (inverse of polling rate).
With a good gaming mouse which has a polling rate of 500Hz or more, mouse delay is fairly insignificant, though. What is somewhat significant in "pro" games, and what I'll try to explain, is what I call the frame delay:
Frame Delay: Delay between last frame rendered by GPU and last frame displayed by monitor.
Say your monitor's refresh rate is a constant 60Hz, and your GPU renders stuff at 60Hz (frames per second, frame rate, or FPS - same stuff),
with some random variance. The maximum possible frame delay is the delay occurs when the GPU renders a new frame JUST after your monitor refreshes.
Time X: Monitor refreshes
Time X + 0.0000000001: GPU renders new frame
Time X + (1/60): Monitor refreshes
…
In this case the frame delay would be nearly 1/60th of a second, or 16.67ms. That's the worst case. On average, the frame delay will be between (virtually) 0 and the maximum possible frame delay, i.e. half of the latter. So in this case this would be 1/120th of a second, or 8.33ms.
Now, with the same monitor, but a GPU which outputs at 100 FPS (again, with some random variance), this delay will be smaller. Now the maximum frame delay is:
(60/100) / 60 = 10ms
And the average frame delay is:
((60/100) / 60) / 2 = 5ms.
Code:
General formula for frame delay:
R: monitor refresh rate
F: average GPU frame rate
Frame delay = ((R / F) / R) / 2
By increasing the FPS above the monitor's refresh rate, one decreases the frame delay. Even though the monitor still displays frames at the same frequency, the delay between the last rendered frame and the last displayed frame is reduced.
By having a lower frame delay, what you see on your monitor is more "recent". You’ll see more up-to-date images of what is going on. For high-precision twitch games like Quake or Counter-Strike, this is a good thing, as the stuff you see corresponds more closely to your last mouse movements.
If you game on a 60Hz monitor and get an average of 60 FPS, you'll have a frame delay of 8.33ms. If you would get 40 more FPS (100 in total), you'd reduce your frame delay by 3.33ms. If that doesn't sound like much, think of network latency, or "ping" as gamers tend to know it by. A 3.33ms delay between what's really going on and what you see is similar to a ping of 33. First-person-shooter junkies tend to want a ping of under 50 and consider anything over 100 to be "laggy". So there you have it: having a higher FPS than your monitor's refresh rate makes a difference.
Note: frame delay has nothing to do with how smooth the graphics look. If your GPU is rendering stuff at around 100 FPS, and it's outputting to a monitor outputting at 60Hz, you’ll still only see 60 frames per second. But, on average, the frames you see will be more up-to-date than if your GPU would render at 60 FPS.
PS: I'm not really sure how V-Sync fits into this all. I know it syncs the frame rate to the refresh rate to reduce "tearing", but I don't know what effect it has on frame delay. I guess a good V-Sync system could force the GPU to render each frame right before the monitor refreshes, minimising frame delay, but in practice it seems to me that V-Sync increases frame delay quite a lot. *shrug*...