I would say that it all depends on the type of grass. Here, we cut Floratam to one height and Bermuda to another.

I have a book authored by the late James Underwood Crockett, a well known horticulturist, which has the recommendations on cutting height and other chores in the maintenance of lawns and groundcovers. Normally, the cutting height is determined on temperature, type of grass and the moisture in the ground. For Kentucky bluegrass, the cutting height is 2 to 2-1/2 inches in Spring and early Summer. When soil temperatures reached 80 degrees, the grass becomes semidormant and does not grow as fast or robust as in Spring. In hot weather, 3 inches is recommended. If you list what type of grass you have and where you live, I'll check my book for the recommendations.