$500 Gaming Rig
CPU – AMD FX-4300 – $89.99
Motherboard – Gigabyte GA-78LMT-S2 Micro ATX AM3+ Motherboard – $35.49
RAM – Crucial Ballistix Sport 8GB (1 x 8GB) DDR3-1600 Memory – $62.95
Storage – Western Digital Caviar Blue 1TB 3.5″ 7200 RPM HDD – $54.99
GPU – PowerColor Radeon HD 7850 2GB – $154.99
Case – Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower – $55.50
PSU – Rosewill Hive 550W 80+ Bronze Certified Semi-Modular ATX – $65.87
Total Price – $519.78 (+$3.00 shipping with Amazon Prime) – pcpartpicker link
At this price point, we’re in a tricky spot for parts. This is definitely one of the harder price points to shop for, and you can have huge swings in your allotted budget (10%-30%) based on current sales, so sometimes it’s a good idea to look around. r/buildapcsales is a good place to start!
The CPU should be fine enough at this price. Obviously a 6300 or an 8350 (or better yet, an i5) would be better, but again, we’re constrained by the budget. The i3 is a competitor at this price point, but for the increased price, it’s not really worth it, especially considering that the 4300 out-performs it in most regards.  
The motherboard is cheap, but it’s fine for what we’re doing here. Same with the RAM, RAM is RAM and this will work fine for us. There’s no difference between one stick or two sticks for purposes of gaming.  The Caviar Blue series of HDD’s will be perfect for this budget as well.  
The Core 1000 is a really good case for its price. There are definitely better cases, but again, price is a major constraint. This case does get the job done, though, if you’re willing to settle for 2 HDD bays and a very small case.  
The PSU gets the job done as well. The 550W Hive PSU from Rosewill is a very good buy for the price. 
Based on the above information, this build should be able to handle most games at 1080p at decent settings. If you start jacking up the AA or something or you try to game at 1440p you’ll obviously run into problems, but all games will run at playable framerates using this build.