Here are the parts:
Graphics Card: This is the main thing a gamer wants. I recommend a Geforce 8600 or 8800
Processor: I would recommend an Intel Core 2 Duo e6600. You can go a bit cheaper, but don't go higher unless you have cash to burn. The price jump is huge, but not the performance.
RAM: 2 GB should do you well.
Motherboard: I believe the nForce are most popular with gamers. I have a nForce 680i and have been happy with it.
Hard Drive: Get what you need. Just make sure it has at least 7200 RPM, or it is too slow.
Disk Drive: You will want at least a DVD-ROM drive so you can install games.
Sound Card: If you like your audio, get a nice one. If you don't really care and just have some junky speakers anyway, you can skip on this, assuming your motherboard has built in audio.
Case: If you have a nice gaming rig, it is going to make a lot of heat. Get a case that has a good cooling system. Getting one with a large fan will make it run quieter (it can run slower if it is larger). You probably do not need or want water cooling, it is a pain to set up.
Power Supply: This will sometimes come with your case. On a good gaming system, you will need a lot of watts- 600 or so is probably a good number to make sure you can expand later. Personally, I like the one at the following link. It is not too expensive, and very quiet- I have to put my ear right next to it to notice it over my other fans. http://www.xoxide.com/aerocool-zerodba-620w-power-supply.html