PC gaming has been around for so long that any system will be able to play games, it's just a question of how old you're willing to go. There are a limited number of new options for you also - your processor could run Modern Warfare 3 or World of Warcraft fine at 1080p!http://www.tomshardware.co.uk/trinity-gaming-performance,review-32533-5.html
As for other games released in the past 5 years of so, most (but not all) will require a little more muscle. Unreal Tournament 3 can also achieve very high framerates on modest hardware and it's a great-looking game.
There are some good threads on here listing some excellent older games that will play on more limited hardware (I'd highly recommend Red Faction Guerilla).
I'm also curious about the decimated one...