EDIT: Weird, my post disappeared.
Useful lil link from the last such thread:
PC Buying Guide
$800 can build a PC capable of running any "good" game, depending on the parts you pick (EDIT: Assuming that you don't have to buy a monitor and OS with that budget too). "Decent graphics" can be bought for as little as $80, although it's usually a better idea to get a mid-ranged card for $120-200. $300-400 is for the high-end range, which are only needed for "decent graphics" in
high resolutions.
So, back to suggesting parts...
CPU: Anything cheap and capable, like the PhenomII series or Core i3/i5 series.
RAM: The cheapest 4GB kit you can find. 1333 or 1600Mhz doesn't make a difference unless you're overclocking.
MoBo: Anything compatible with your chosen CPU. MSI, Asus and Gigabyte are good manufacturers to look for (and I personally hate AsRock).
GPU: Something midranged, like the HD5770, HD6870, GTX 460 or GTX 470.
Case: Whatever looks good to you. I use an Antec 1200 because it can fit anything inside (i.e. the best graphics cards when I'm testing them) and has awesome airflow. Smaller and cheaper versions exist too.
PSU: Anything between 550-700W is good, so long as it has a well known brand. Non-branded PSUs usually smoke/fry/explode, seriously.
HDD: Samsung Spinpoint F3. Anything between 500GB-2TB, depending on how much money you want to put towards it. HDDs are cheap anyway.
ODD: Any cheap $18 DVD burner.
Things to consider: games depend on the graphics more than the processor. Intel CPUs handle around 30% more IPS (which is important for gaming) than equivolent priced AMD CPUs. SandyBridge CPUs (which'll also be called Core i3/i5) are being released in a week, so it may be worth waiting to see how they perform in benchmarks.