PCPartPicker part list:
http://pcpartpicker.com/p/3ncpz
Price breakdown by merchant: http://pcpartpicker.com/p/3ncpz/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3ncpz/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($72.98 @ OutletPC)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($63.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($54.98 @ OutletPC)
Video Card: EVGA GeForce GTX 760 2GB Video Card ($249.99 @ NCIX US)
Case: Corsair 400R ATX Mid Tower Case ($69.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($59.99 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $791.87
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-06 18:14 EDT-0400)
A little bit close to the top of your budget but should be able to run all games on high-ish settings.