Ok, exactly how much does CPU performance matter when you're playing games? Is performance here mostly a video card thing?

If I've got a system with a nice video card (Radeon 9600) will a 1.6 Ghz Pentium III - M be holding me back?

Umm...yeah! The new Radeons and GeForces were made to pair with high end CPU's like the Athlon XP's and Pentium 4's. And since CPU does mean central processing unit, is a good CPU important? It better be. The new generation of gaming is really video card dependent but if you don't have a good CPU to pair with that video card then it's game over.

CPU Performance does matter, but I think the processor you're using now is good enough. But say if you upgrade your processor to a 3.0ghz P4, you will get a huge performance boost in gaming and applications/programs. Another way to get a performance boost is by getting more RAM since memory is very important, you should have at least 512mb for gaming.

Asus P4S800
Pentium 4 2.6ghz @ 3.0ghz
eVGA Geforce FX 5900 SE
SB Audigy LS

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im running a Pentium III 800mhz (dont laugh)...with a nVidia TNT2 Riva 32mb...counter-strike and starcraft are like the only things that run perfectly...o wait not even counter-strike i get a low 72 fps...

Your videocard is one of the better ones atm.
Your processor could use a change. Buying a new one would help get more out of your videocard. Stuff like fps would increase and if you are experiencing shocks in Shooter games this would certainly help.
Your memory is a bit low. Upgrading to 512mb at least would help a lot. You would see a huge increase in speed when your cpu has to calculate stuff. Because if your computer can load more mb at a time the more quicker the computer will be.
You didn't mention how quick your harddisk is. This part is probably the slowest part in computer at this moment. But for games allmost only loading times would be smaller.

And E-Weezy. Why laugh? that pretty normal for a 800mhz. If you don't play games or use programs that "need" better computers to work SUPER why bother :)

to increase computer performance its a combination of a couple of things, such as:
processor
memory
video card
hard drive speed and access time
the FSB on your motherboard and cpu

FSB is the time it takes for the cpu to communicate with the other devices, like video card, memory, etc.