If you are looking to replace your CPU only (no monitor) 800 is a ton to spend.
You require pretty basic stuff that almost any computer will do and do quickly. You should ask yourself, how much do you want to spend? and how long do you want to keep it?
I've been pretty happy with Dell and just purchased my second Dell 3-4 months ago.
If your budget is 800 bucks or so for just the PC, like EVERYTHING fast, do not anticipate playing games, anticipate that you will continue to use the PC in the same way (email, bets, porn, surfing, etc.), and want it to last 3 years or so without feeling the need to upgrade... then get a 2ghz+ Pentium 4 with 256 ram and you will be very pleased. Skip the extended warranties, skip the DVD writer (do get a CD burner), skip the advanced graphics cards and such.
The PC described briefly above will give you room to expand if necessary while giving you current technology which will be good for the future. It is WAY more than you need today though (for example you do not need a 2 ghz p4 to surf and send email). If budgetary concerns are an issue then you need to post how much you have to spend and whether or not you need a monitor and I'm sure the geeks will come out and design a pretty sweet machine for you.