I just unloaded a couple Sapphire 7870 Ghz Edition GPUs to replace with something newer. I started with just one and it ran Skyrim very well - smooth @ 1080p with everything maxed. They are running about $75 used on eBay, and still handle newer games pretty well. I played Shadows of Mordor and Alien: Isolation on one of those last fall and both ran great.
For reference, I have an i5-3570k CPU. Keep in mind that an older or weaker model CPU can be a drag on certain graphics cards.