It's not going to break any records but here's a build for $578. It doesn't include any peripherals like mouse/keyboard, or a monitor, and you'd need an OS, but it's a decent start for the money.
PCPartPicker part list:
http://pcpartpicker.com/p/3s9Vg
Price breakdown by merchant: http://pcpartpicker.com/p/3s9Vg/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3s9Vg/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($35.98 @ Newegg)
Motherboard: Asus M5A97 R2.0 ATX AM3+ Motherboard ($89.79 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ Newegg)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($50.10 @ Amazon)
Video Card: MSI Radeon R7 260X 2GB Video Card ($119.99 @ Micro Center)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($37.99 @ Micro Center)
Power Supply: Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply ($53.98 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.98 @ OutletPC)
Total: $577.79
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-15 11:09 EDT-0400)