I find that I have to top off my 700 x 23 tires every day or two in order to avoid pinch flats (I run them at about 120 psi). Fatter tires will run at lower pressures without pinch flats, so I can pump them up to max pressure and ride for a week or more before I have to top off the pressure. Ever try to get a tire up to 125-140 psi with a frame pump?
And, like everybody said, spoke reliability, pinch flats, comfort and speed on rough roads, tread life, traction on dirt roads or in the rain, etc., etc. If you're a weight weenie there are kevlar beaded tires in wider widths if you look around, and Schwalbe makes extra light tubes for fat tires.
I run 700 x 23 on my road bike, 26 x 1.75 on my tourer when I'm carrying camping gear, and I'm going with 26 x 1.6 for an upcoming credit card tour.