I'll tell you what. Right now I am running 5 clients with my 5 year old pc.
AMD Athlon 64 x2 5200+ (2.6ghz)
4GB DDR2 (Not sure of the speed but its not the top)
1024 MB Nvidia 9800GT
Win 7 x64
My 5 clients with graphics at bare minimum run without a hitch, I can push the graphics up a bit if I wanted, but larger fights start slowing it down. I could probably add another client if I wanted and it wouldn't be to bad.
So my guess is that pretty much anything nowadays can churn out 10 clients with the right video cards. My buddy is getting an inheritance soon and he wants me to build him some crazy things so I am staring at those i5's. I built a different custom i5 for another friend and when we first fired it up we turned on and logged into 7 World of Warcraft accounts at max details before it finally started to hiccup.
It all boils down to the video processing capabilities of your machine when multiboxing. Minimum graphics and pretty much anything aside from a celeron can run 5-10 clients, but it will need a hefty video card. Consider going relatively budget on the pc, but spend more money on video and maybe do some research on sli and xfire (Ati and Nvidia respectively), I have no personal experience with it and I keep getting mixed reviews.
Look for mobos with at least 4 ram slots, PCI-e video is MANDATORY nowadays, and avoid the cheapest cpus, go with at least an AMD 64, or intel i series, you can get them cheap enough and it is well worth the extra penny.
Here is one I found its a good start (poo on Newegg)
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=7192180&CatId=4910
Throw in decent video card and double the ram and good to go. Maybe a little closer to $600, but WELL worth it to get the i series