Some advice from a Hardware God...
Qualifications: I've been building my own computers since 1995. Worked at a computer store as a technician for 1 1/2 years, then went to work at Microsoft. One of the first people to overclock their Pentium, AND I've been Intel-free for ~4 years now.
Some general pointers:
1. Know what you want to do with your computer, and build around that idea.
2. Get the most reliable components over the fastest. Some web sites talk about how great something overclocks, but frankly, if it's not on the WHQL list, there's something wrong with it most likely.
3. Don't get parts that lock you in to a single vendor. Dell, Compaq, HP, Gateway all want you to throw away your computer and buy a new one instead of upgrading it. Gateway isn't quite as guilty of this as the others, IIRC, but I haven't bought a stock computer in some time.
4.
http://www.newegg.com
Nope, I'm not an employee, I've just bought a lot of stuff from them, they have excellent prices, excellent policies, and are a pleasure to work with. The couple times I've had to send something back, they've been REALLY good about a fast turnaround with the replacement part. They even credited me once for a part that was no longer under their warranty, but under the manufacturer's warranty, something they didn't have to do. I am *VERY* happy with them.
5. Don't buy winmodems if you can help it, unless you need one only for limited use. (I have one that I only use for fax services) They suck up CPU time, and are horribly inefficient.
6. Memory, memory, memory, memory! Games especially will suck memory out of your system like a vampire. If you can get it, go with 512mb, if not, 384. 256 is bare minimum these days.
7. Go with Windows 2000 instead of XP. XP is a bloated pile of crud with no real redeeming features, and a higher price tag to boot. I should know, I worked as a software tester at Microsoft during the XP test cycle.
8. NVidia is the One True Video Card Manufacturer for now. ATI makes nice hardware, but their drivers suck.
9. Sound is a weird thing. I *REALLY* hate Creative Labs right now for reasons I'm not going into (that would be a whole thread, but basically they have killed a bunch of new tech so that they could remarket the same crap year after year...) so find something else OTHER than a Creative Labs product. Problem is, there's not much else out there that works.
10. Don't buy Intel. AMD is much cheaper on a performance/$ basis. Not only that, but there are ZERO compatability issues. Intel JUST reclaimed the performance crown (barely) but the processor costs 2x as much as AMD's most expensive processor. AMD is a bargain. (Note: I own stock in AMD, and it's in the crapper. I've lost 50% of it's value, so I do have something to gain by saying this.

Even if I didn't own stock in them, I'd still tell you to buy AMD.)
11. Build it yourself! You'll learn a lot about how computers work in the process... But if you don't want to, there are a lot of people out there who will help you.