CPU Intel Core i3 3220, Motherboard AsRock Z77 proM , RAM 8GB of kingston hyperX, Case Bitfenix Shinobi Mid-tower case, GPU MSI 7870, PSU Thermaltake TR-500PCAU TR2 500W 80+ bronze.
Would an AMD build be better? What should I replace? What games will this be able to run? I do not have an optical drive or hard drive in here as I alredy have them.
It is a good build definitely, here is what the 7870 can do in games: http://www.anandtech.com/bench/Product/548
The GTX660 is also compareable in price to the 7870 and plays a few games better, some games it gives you better fps while on others it does not, here is a bench of both: http://www.anandtech.com/bench/Product/548?vs=660
AMD build would probably give you a stronger graphics card for your money, depending on the processor you pick of course.