Okay, so I got the build to $774 with a GTX 770, which will play almost anything except the most intense games (such as Crysis 3) at max or very close to max settings for 1080p while still maintaining 60+ fps for the most part. The only one I've had any issue in my own library is Assassin's Creed 4. I can still max out AC4 but it's usually in the 30s or high 20s for fps with my 770. (I have no personal experience with any recent AMD video cards so I'm not sure how they stack up, but I'm sure a comparable AMD card is fine, such as the 280x)
PCPartPicker part list:
http://pcpartpicker.com/p/3u7eB
Price breakdown by merchant: http://pcpartpicker.com/p/3u7eB/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3u7eB/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 ($29.98 @ OutletPC)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($73.98 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($74.98 @ OutletPC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: MSI GeForce GTX 770 2GB Video Card ($319.99 @ Amazon)
Case: Cooler Master Elite 430 ATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: Corsair Gaming 600W 80+ Bronze Certified ATX Power Supply ($69.99 @ Micro Center)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($15.00 @ Newegg)
Total: $773.89
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-18 17:28 EDT-0400)
If you absolutely have to be under $750, then you need to step this build down to a GTX 760, which won't run most modern games at max settings 40+ even at 1080p(you'll have to drop it down to medium/low), which is why I stuck with the 770 even though it's a little bit beyond the budget.