This depends on the type of dvi connectors you have. With single link DVI you can get resolutions essentially upto 1920*1200. To get to the 2560*1600 resolution you would need to have dual link DVI connectors. And the correct cables of course.
But as for "the best video card", the high end models support the 2560*1600 resolutions with DVI connection.
Dual link DVI is limited to around 2560x1600 at 60Hz, as noted here: http://www.datapro.net/techinfo/dvi_info.html
Technically, that is not the max resolution; it can go slightly higher at 60Hz, but there may not be any monitors out there with a slightly higher resolution, so that's probably why they say 2560x1600 at 60Hz.
Also, you might be able to double the resolution if you run at 30Hz... meaning you could run quad hd (and maybe 4k resolutions) at 30Hz, but I could be totally wrong about these two resolutions.
Here's the calculations:
*. DISCLAIMER: Technically, the way I calculated below is not the true max resoluion. To find the true max, you need to calculate the actual bandwidth of the cable and DVI spec and take into account blanking overhead and maybe other factors. My calculations below do not do this, so may be wrong. http://www.molex.com/mx_upload/family/microcross_dvi/Co...
1a. Single link DVI supports 1920x1200@60hz
1b. (1920 x 1200 x 60) = 138,240,000
2a. Dual link DVI is double single link DVI.
2b. So: 276,480,000 (138,240,000 x 2)
3. 2560 x 1600 x 60 = 245,760,000 so it works on dual link DVI.
4a. 4k = 4096 x 2160
4b. 4096 x 2160 x 30hz = 265,420,800 So a 4k resolution at 30Hz might be enough for dual link DVI. However, if you have to add "blanking" numbers and/or other factors, it might not work, so I could be wrong on the 4k and/or the ulta hd resolutions.
So, to get higher resolutions at 60Hz, you have to use Displayport 1.4.
(hdmi 1.4 may not work: For example, the hdmi site shows support for 4k only at 24Hz and quad hd up to 30Hz using hmdi 1.4.)
I should also add, that I wonder if maybe the reason some video cards list 2560x1600 as the max resolution is because of the limits of DVI. ... and by that same logic... I wonder if you used Displayport, if those same cards could go higher. (I don't know the answer).
July edit: fixed some things I said that were wrong; added some correction details.