I 4-boxed (Everquest, not WoW) using a Radeon HD2600XT 256mb on a Q6600 quad core processor. The HD 2600XT seems to be considered the bottom end of the "serious" graphics cards, per Tomshardware (as in, the cheapest true gaming card you can get). It worked smoothly with the graphics settings all near the low end, I never really tried turning everything up with it. I'm now using Radeon 4850's to run 6 accounts (4 on one computer, 2 on another...will probably do 3 and 3 eventually) with everything set on high (2 1080p monitors), and it's, so far, working very well.

I'm sure WoW's a bit different, but just throwing in my 2 cents if it helps give you any idea. I've always been of the opinion that the graphics card isn't as important as the RAM when multiboxing, and as others have mentioned, the processor and HD configuration.