Source: http://www.gamersnexus.net/news-pc/612-players-dont-meet-bf3-recommended-spec
GTX 580/AMD 6990: You will be able to play at maximum settings and possibly even be able to support multi-monitor setups (though may require reduced shaders or AA).
GTX 570/AMD 6970: You can play at near-max, if not max, settings but will not easily support multi-monitor or 3D effects without decreasing quality.
GTX 560/AMD 6870: You will need to reduce anti-aliasing and ambient occlusion; you may need to reduce shaders on large servers.
GTX 460/AMD 5830: You will need to massively reduce anti-aliasing and may need to disable soft shadows, bloom, or other atmospheric effects.
GTX 8800/AMD 3870: You will need to reduce or disable the following options: atmospheric bloom, atmospheric smoke, high-dynamic range lighting, soft shadows, ambient occlusion, anti-aliasing, and motion blur.
If you want to play with 3D Vision (we reviewed it here) or other 3D technology and still maintain ultra (or near-max) settings, it will likely require 2xGTX 580s to maintain your quality. Other factors, such as multi-monitor setups, may call for more powerful cards, like the 590.