This computer is not exactly high end, but by all means, any game you give it should be perfectly playable. Unless you are addicted to high resolutions and mass frame rates, this is perfectly suitable for anyone who wants to play Minecraft, WoW, any given game on Steam, etc.
Remove the 2 250gb HDDs, if you need more hard drive space, just go for a 3TB or stay at 2TB (Also, check up on the RPM of your hard drive, that can play an important roll in single player games and all over modify your performance. I'd vote at least 5400rpm, but go for 7200rpm), and definitely look into an SSD, they are well worth the investment. Your processor is entirely sufficient, as is your graphics card, for gaming, anything more powerful is likely to just be overkill. Your motherboard is okay, but DO NOT go cheap on your motherboard by any means. It is probably the most vital factor in making a computer suitable for what you want. To finish this section off, 8gb of RAM clocked around at least 1600MHz is perfectly fine for almost anything.
Also, using Windows 7 Ultimate will merit you no benefit in gaming, so unless it is coming free of charge, I'd cut out that bit of the package.
Good luck with that =)