AMD's display output logic is clearly superior to what NVIDIA has to offer at this time. Vendors are free to combine six TMDS links into any output configuration they want (dual-link DVI consuming two links) - and use them all at the same time. AMD has also introduced DisplayPort 1.2 support with their new cards which allows the use of a DisplayPort hub to connect multiple monitors, or daisy chain them together.
so yes, they support 6 monitors, BUT you need to daisy chain displayport monitors in order to do so, since most cards only have 2 DP outputs (or use a mst hub, though I haven't seen any yet). And for the daisy chaining you might need some funky cables, not sure exactly how it is done...
amd promo slide, 2 dp outputs, six displayshttp://www.techpowerup.com/reviews/HIS/Radeon_HD_6870/images/slide7.jpg
"DP 1.2 monitors have 2+ ports, with which you can connect up to 3 monitors in serial. Two ports on the card, so 6 monitors that way. You can do this only with native DisplayPort 1.2 supportive monitors. No DP-DVI dongles work. "
so you need funky monitors rather than cables :P