Okie, lets make things simple.
For a gamer, in order of importance:
Graphic Card
RAM
CPU
PSU
On the other hand, this list is useless. Any of those that is bad will draw back your system. Therefore, these 4 will need to be quite equal in terms of specification.
For a demanding game to be run, you need enough processing power. However, you dont need a top of the line processor to run most games now. A Single core 4000+ or a Dual core 3800+ will do the job now. Even if you increase the CPU to a FX 60, the difference will be trivial.
Also, you need decent graphic card and decent RAM. For most games now, 2gb of RAM is enough. 1GB of good RAM can be alright, but only if you Overclocks them.
The thing that people spends most money on is the graphic card, and gamers they change their graphic card almost every 3 months (but not CPU or RAM). The money that you are going to spend on your graphic card depends on you budget, your other system components and your screen. No need for superb graphic card when you run it on a 15'' screen. On the other hand, you do need a good one.
For PSU, it supplies power to your whole system, therefore you need a strong and stable PSU. A cheap PSU can damage you system, which might cost you some 1000$ in a second. So be aware. If you really want to game seriously, you need more than 500 W power. 430 W can be fine, given that you dont have too many drives, huge cooling system, and of couse you are running a single graphic card. To run SLI, for example, a 480W PSU is the minimum requirement.
Other than that, a good mobo is needed as well. Good mobo can help you to overclock easier, and more importantly, to upgrade in the future. A non PCI _E mobo, for example, will mean that you cand install a PCI-E graphic card, meaning that you are unlikely to run games in 1-2 years's time with satisfactory resolutions.