Budget? What games do you want to play?
Anyway, no, this PC wouldn't be able to handle very much, maybe on lower/medium settings but for $1000 you should be looking at getting ultra settings on newer games....
You made some really strange choices, I'll just run through them.
PCPartPicker part list:
http://pcpartpicker.com/p/nyMZ99
Price breakdown by merchant: http://pcpartpicker.com/p/nyMZ99/by_merchant/
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($189.99 @ Amazon)
CPU Cooler: Thermaltake CLP0605 79.3 CFM CPU Cooler ($28.50 @ Amazon) - Get a Hyper 212 Evo, similar price but better
Motherboard: Asus Z87-Pro ATX LGA1150 Motherboard ($149.99 @ Newegg) - way too expensive for your other components
Memory: Kingston 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ NCIX US) -Good choice
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($58.97 @ Mwave) -Quite small but okay
Video Card: Asus GeForce GTX 650 1GB Video Card ($111.98 @ SuperBiiz) -This is a really weak card, in a gaming PC the GPU should be the most expensive component
Case: Thermaltake Urban S21 ATX Mid Tower Case ($63.06 @ Mwave) - Not too bad of a choice
Power Supply: Thermaltake Smart 630W 80+ Certified ATX Power Supply ($81.38 @ Amazon) -Way, way overkill for your current build. PCpartpicker's estimated wattage is 250W, why would you need a 630w PSU
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($16.01 @ NCIX US) - This is fine
Operating System: Microsoft Windows 7 Ultimate SP1 (OEM) (64-bit) ($187.97 @ OutletPC) -Windows 7 ultimate is much more expensive and you're not going to use many of the added features so it's just a waste of nearly $100
Total: $962.84
Prices include shipping, taxes, and discounts when available
Hang on a minute while I get you a better build