I would vote against this idea.
each monitor you add to the setup is more GPU/CPU you need in the PC, the higher the resolution of each screen the more GPU/CPU you need as well.
so I'm guessing a motherboard with 3x PCIe 16x slots, each card handling two monitors.

The problem I see with this setup is your memory bandwidth to the main memory is fixed and at some point the video cards are going to need more bandwidth that main memory can supply.
the same goes with the main CPU, even a quad core ( or the sudo 8 core i7 ) only has so much CPU it can give to each of the 5-6 games you are going to be doing.

three boxes with one video card each has 3x the main memory bandwidth and 3x the CPU bandwidth.
I've tried running 5 copies of wow on a single box with a GX280 and I find I have lag, using two PCs ( one with just an 8800, the other with GX280) with 2 copes of wow on one and 3 copies of wow on the other and I rarely have lag
when using 3 pc ( 8800,8800,gx280) I never have lag.
the slower PC only have 2.4Ghz quad cores and the big machine has a 3Ghz quad core.
It's from this experience that I find I don't want to make a monster machine, I prefer my 3 box setup over one monster PC.
I also find that when doing 3x PC I find I don't need a monster video card or the most expensive CPU.