Basically, any video card with a fast enough RAMDAC can handle that resolution. They do run that at a very low refresh rate of 40-something Hz, so although you don't see any flicker, screen update speed isn't going to be the greatest, and you can forget any kind of gaming on that thing (can your Radeon 9700 get over 40 FPS in 3840x2400, after all? 😉).
The intended uses for that are probably not things that you would be doing at home (medical, scientific, and other visualization applications), but I will admit to wanting one anyway, just for the coolness factor! 😛