Quote Originally Posted by Tonuss
That should be plenty for what you are describing. I run one account on a Core2Duo 6600 @ 2.4GHz and four accounts on a 2.2GHz dual-core Athlon XP with 3GB memory and a GeForce 7800GTX with a 20" monitor. I have four 800 x 600 windows tiled as best as I can (very slight overlap). With all graphics settings at their lowest, they run at ~20-25 FPS with noticeable stuttering, but everything works.

I'm going to upgrade that second system with a 2.4GHz quad-core CPU now that they're relatively inexpensive. I may upgrade the video at some point but it should do just fine for now.
Just thought I'd update this. I upgraded the dual-core Athlon with a 2.4GHz quad-core Pentium yesterday. Turned out the older motherboard used DDR memory and the new one uses DDR2, so I went from two computers with 3/4GB memory to two computers with 2GB memory.

However, upgrading to quad-core has made an enormous difference. The four windowed WOWs run smoothly and at 70-85 FPS most of the time. The video card is the same and the memory has actually been reduced, so it seems that a relatively inexpensive CPU upgrade (~$270 for it, motherboards can run $100-220 or less) can provide the biggest benefit for running multiple WOW accounts on one computer.