I haven't had many flats, but with my aluminum-framed bike I was tired of the jolting and buzzing over rough roads and ended up going to more of a hybrid-bike tire -- a 700x30 that I run at 85psi and really smooths out the ride. Surprisingly, I can't feel any difference in rolling resistance and am riding at the same speed as usual.
My bike is a Specialized Sequoia that has the clearance to run this tire, although I had to change out the brakes to a model that opens wide enough to let me get the wheel off without having to deflate the tire.