It's kind of a playable vs. max settings kind of thing.
I can run wow on my 6 year old laptop but it'll look like hell. Playable, but ugly. Doesn't take much. At max settings in certian reigons i was getting a framerate of about 35-40 even with my computer. (8gb ram, hexcore processor, gtx570). Decent graphics are important for a few bosses, and good frame rates are important for all of them.
Also, Wow is about to get another expansion before too long which means graphics updates to existing content and new zones built with improved graphics in mind.
So while you don't need a top notch graphics card? a good one is quite useful.