I've got a 5870 2GB card, 8GB of system RAM, a Phenom II 3.2Ghz 6-core cpu, and a regular 7200 RPM Western Digital HDD, and I can run it literally maxed out (with the exception of the anti-aliasing and anisotropic filtering settings being off, 'cause of the current problems with those. I have yet to try setting them up high in Catalyst Control Center.) I haven't actually CLOCKED my fps with anything, but it's gotta be at least 40, if not higher. I barely notice any occasional kinks in the framerate, and even when those occur the framerate still always levels back out within a second at a VERY smooth number, whatever it is.
And just for the record, I can also run BF3 on a blend of high and ultra settings, and it runs quite smoothly for me as well, even in huge multiplayer matches while I'm surrounded by explosions and air support.
So, to anyone trying to figure out how good of a system they need, mine cost $1000 a year-and-a-half ago (so probably about $6-700 now, maybe), and I can STILL run these newer games, perfectly fine, not on crappily low settings. So, yes, if you've got even a SINGLE 6000-series Radeon card, and it's got more than 512MB of VRAM, I'd imagine you should be able to run lots of stuff on nice settings, so long as you've got a decent quad-core CPU and some nice system ram backing it up.
Most of these setups people say you'll need to run new games on high settings are SERIOUSLY overkill. If you WANT that much horsepower in your system, then more power to ya. I just think it's not very cost-effective to get all brand-new technology if you think you NEED it so your computer won't be outdated in a year. The price of brand new stuff seems to drop about 50% in a matter of months, and if you buy stuff that's still pretty new but doesn't cost as much as a car, you can still put together a system that'll easily get the job done for a few years, and can be easily upgraded at that point when it finally starts to struggle a bit.