Now this may not be an ultra cheap build, but I can guarantee that it will play any game out there @1080p (not all ultra settings). You could go cheaper with the build the guy above me mentioned, however that CPU is really outdated and if you wanted to upgrade to an i7 or something you would then have to swap out your motherboard, CPU, and possibly RAM.
PCPartPicker part list:
http://pcpartpicker.com/p/QrMFpg
Price breakdown by merchant: http://pcpartpicker.com/p/QrMFpg/by_merchant/
CPU: Intel Core i5-4440 3.1GHz Quad-Core Processor ($169.99 @ SuperBiiz)
Motherboard: MSI H81M-E35 V2 Micro ATX LGA1150 Motherboard ($59.49 @ SuperBiiz)
Memory: G.Skill Ripjaws X Series 4GB (1 x 4GB) DDR3-1866 Memory ($33.99 @ Newegg)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 750 1GB Video Card ($79.99 @ Newegg)
Case: DIYPC MA01-G MicroATX Mini Tower Case ($24.99 @ Newegg)
Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply ($29.99 @ Newegg)
Total: $448.43
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-12-22 10:42 EST-0500