Minimums:
Intel Core 2 Duo (not Dual Core)
4gb RAM (more is great, too)
320gb HDD (more is great, too)
NVIDIA or ATI graphics card. Google the card. notebookcheck.net (or something like that) will tell you how well that card holds up with games. I believe it compares each card to Crysis and tells you how well it will run it (if it can run Crysis, it can run anything).

I think there's something called "Alienware" that's made specifically for gaming, but beware - gaming computers cost more than any other. If you have no price limit,
Intel Core-something-Quad. IDR if it's called Core2Quad or whatever, but it's like the Duo but twice as better (thus epicccccc)
8gb RAM
1TB HDD
NVIDIA/ATI high end, probably would cost $500 extra
That would probably total from the upper one-thousands to the lower two-thousands. Not sure how much a Quad processor costs, but I assume it's ~$500. I don't know of anyone who has one, but if you do, your computer will run faster than anything ever. Also, there's something called Intel i7, I believe. IDR if it's a Quad ore Duo processor, but it's supposed to be really good - one of the latest processors.

Also, if you get a Core2Duo, don't get anything less than T6xxx (e.g. T4xxx). If you can, get a P series (or the one after that, that IDR). The P series uses very little electricity, so saves money, but costs about $50 to $100 more than the T6 series.

Oh, and if you don't get a gamer desktop, I'd recommend custom building it (via an online form; not ordering each piece separately). But I think all of Alienware desktops are made for gaming. I may be wrong.