I built a computer in general, not necessarily for gaming, but I do play games a bit. Before shipping and taxes this build is $380, with shipping and taxes it was $460 (I live i canada and the shipping is like 2x more than US)
AMD A8 5600K APU - $100
2x4 DDR3 1600mhz (oced to 1733) - $20
ECS A75F2-M2 mobo - $80
Thermaltake V3 Black edition case - $30
Radeon HD 6670 1GB GDDR5 (In dual graphics mode with my APU) - $80
Life time series 500W PSU - $20
Western Digital Caviar Blue 500GB 7200RPM HDD - $50
Shipping/taxes - $80
I can play these games on 1080p
Battlefield 3 on ultra (turned off AA and AF) - 40 fps AVG online
Skyrim on ultra - 35 fps Avg
Fallout NV on ultra- 60 fps Avg
GTA IV maxed out- 40 fps Avg