There are definitely a lot of good suggestions here. I think I'm going to add a little bit of two sense here.
1. It's been mentioned a lot, but computers are only as good as the parts you buy - if you buy quality, brand-name parts, you will find that your experience (in the long run) will tend to be more stable and you will experience fewer earthshattering issues. If you skimp on parts, you get what you paid for (most of the time). There is nothing wrong with some of the cheaper brands...except that you run more risks. Even good brands c**p out...so don't fret it if it does happen (ruins the experience)
2. Be patient. Your first build is not going to be a GOD machine (thought you might get lucky...I had a pretty good one...after two years, it was still hanging with the mid to high end machines DELL was selling. Try to avoid shooting for overclocking on your first machine (at least wait until after you build it to worry about it). Too many people try to jump straight into the overclocking before they've even had the experience of building a stable and working machine. It can easily ruin your experience (man...I sound like some grumpy old guy telling some teenager to slow down...must be cuz I'm getting old at 22).
3. THERE'S A REASON IT'S CALLED A MOTHERBOARD!!!!!! Don't even think on skimping on this piece of hardware. Look at the specs. There are more integrated features and hardware in a motherboard than in ANYTHING else on your computer. Don't be an i***t. Buy a good motherboard. Read reviews. If you have never built a system before, do as others have said before in this thread...read the negative reviews. Look for the technical reviews where someone explains the problem (the single-egg posts are worthless if they are written just because the board was DOA...that comes from an impatient kid who is just p****d off. It won't help you judge a board). Another thing you may want to strongly consider on your first build is buying a MOBO that's a couple months out of the door. That gives the manufacturer plenty of time to RMA all the bad boards and fix driver issues (Obviously, if the board has had LOTS of driver issues, you just might want to avoid it altogether).
4. Backbone parts - Without the backbone/supportive parts of a PC, your CPU is useless. Get an AWESOME power supply (but don't spend $1000 on one...give mommy her credit card back). Make sure the power supply you buy has REALLY high ratings. Maybe even take the time to see if Tom's Hardware, HardOCP, AnandTech or other hardware reviewers have checked it out. Your power supply is worth every penny you put into it.
5. So is a good case and fans. My favorite case that I own is my Thermaltake Armor (whichever the original one was with the 25cm fan). I don't even use the 25cm fan because it stays cool without the fan as it has four others that work GREAT. It's been the best $50 dollar investment I've ever made, especially since I got it on special, with a rebate, and the prices for Thermaltake Armor cases have stayed pretty much the same since.
6. Next, choose good memory. Also, make sure you have enough memory. Applications are rarely processor-bound nowadays (that's the technical term for "You don't need a fast processor as much anymore to get the same performance"). Programs now are extremely memory-intensive. Now that so much is written in Java, (*cough)memory leaks(*cough), and scripting languages, and since graphics is screaming for more memory all the time, it is imperative that you buy LOTS of good memory. Don't waste your money buying the latest and greatest memory unless you have built before (no matter how much you think you know about computers, it all changes when YOU are the one maintaining that fine balance between barely-working parts and a smooth-operating, well-oiled machine).
7. The CPU is the last thing you should worry about building a machine. Obviously there is some sort of balance between a good processor and the rest of the equipment, but you can get away with a slow processor and you'll still have a fast machine. Don't buy some screaming processor thinking that it is the most important part of your computer. Make sure you surround the processor with quality parts. In fact, you should collect those parts first because the CPU is rarely the bottleneck.
8. Research. Once you think you know what you want to buy, Look at reviews for every part. Make sure that they all have GREAT reviews. If so, knock yourself silly. If not, you may want to revamp your blueprints.
9. Don'y underestimate brand affinity. While not always the case and definitely not a hard and fast rule, you may find that, often, parts from the same company just seem to have that mysterious quality that they just work together well. Nobody really knows why...except maybe the people with too much time on their hands...but buying an intel board for an intel processor just makes sense. Buying AMD/ATI stuff seems to work well (in fact, I am personally of the opinion that AMD/ATI stuff just works smoothly without quite as many hiccups...the parts seem to like each other).
I got lucky on my first build...I did my homework and my computer meshed together well. I had a buddy that built his first computer about the same time I did and he wasn't so lucky. your first experience will vary, but don't be disheartened.