You can't afford this month's rent, but you DO have enough to upgrade that old HP Pavilion with the Pentium 4 @ 1.4ghz (What's a Willamette, anyway?).
Seriously though, this is for the people who have a neice/nephew who wants to play wow, or some other older games. Budget is tight, and you just want something with the absolute bare minimum. Corner cutting, cheaping out, and generally being a penny pinching bastard, this is what we're looking at. But don't think that Scrooge McDucking your way through life means you have to get crap. The posts I'll make on here are an effort to be both quality parts, and also the best bang for what few bucks you have.
Systems posted on here may have specials, promotions, and coupons, and may not be as cheap weeks from now. I'll try to update stuff as I see deals.
PCPartPicker part list
CPU: AMD Athlon II X4 640 3.0GHz Quad-Core Processor ($72.74 @ Amazon)
Motherboard: MSI 880GMS-E41 (FX) Micro ATX AM3+ Motherboard ($29.99 @ Newegg)
Memory: Corsair 4GB (1 x 4GB) DDR3-1600 Memory ($19.00 @ Amazon)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($57.98 @ Outlet PC)
Video Card: Gigabyte Radeon HD 6670 1GB Video Card ($56.97 @ Newegg)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($34.21 @ Amazon)
Power Supply: Corsair Builder 430W 80 PLUS Certified ATX12V Power Supply ($24.99 @ Newegg)
The CPU is probably the most cost efficient CPU there is, at the lower tier. 4gb of ram is really all you need to play WoW. Multitasking is really not a big focus here. A 500gb drive is more than enough for anyone without a movie collection, however any smaller is almost the same price. The 6670 GPU is weak, but certainly strong enough to run WoW pleasantly on medium settings. The case and power supply are nothing special, but still good quality build. The Corsair CX series is usually nose thumbed at, however the power requirements of the system are so low it doesn't matter. There is currently a sale to knock it down to $15. No DVD drive. Make an ISO of your OS and use a $5 flash drive to install windows.
CAN IT GO CHEAPER?
Certainly, however cheaping out any further on certain parts would drop the system's performance more than it's worth. I bet I could shave another $50 off this, but it's usability as a game system would drop faster than the hamiltons.
EDIT: I actually put together pretty much a Bottom of the Barrel system. I wouldn't really recommend it for gaming, but I SUPPOSE it could play wow. It could certainly do normal internet stuff and act as a business machine, and flash games and stuff. It'll set you back about $210 without the OS.