My setup:

Intel Core 2 Quad Q6600 2.4Ghz
4 Mb Ram
Vista 32
Nvididea GeForce 8600 GT
One 24" Monitor

I run 5 Wow's without major problems, with gfx on high on the main screen and mainly low on the minion screens. Could be better at around 25-30fps on all screens when out and about and around 15fps in cities, but it's playable.

I'll most likely look to upgrade to a nice 8800 card after the prices come down to below £100.

If in doubt, set up a few trial accounts and see what the performance is like.