If you're going for cheap, check out my sig.
I am running an eMachine (yes, eMachine) that I bought two years ago at WallyWorld for $494, including monitor. I have bumped the memory from 128MB to 512MB (about $70). I have added a DVD drive (WallyWorld, $45). And I have dropped in a graphics card (an old one, $60 @ Best Buy).
If you add it up, you get $669, but the components would be dirt cheap right now, if you could even find them. I have run HL2 on this thing, so I know it doesn't take a fortune to build a decent computer.