I have always mowed at 3.5" most of the year, but much closer in the fall so I can reseed. This year is the first year I have stepped up to 4". The results are surprising. The yard is so plush and green. Just before I mow, it looks like the "Bliss" desktop on windows. After I mow, it looks like a traditional yard, only better in my opinion.
After a serious dry spell a couple of years ago, I had to get very serious about the yard, since I live on a hill. Part of getting serious was deciding what the yard is "for." I like it to look nice, but I need it to be resistant to dry spells, but most importantly, I need it to keep my land within my boundaries, and out of the flow of water. I am hoping that the 4" height will be the best of all worlds. So far, it is very pleasing to the eye.