My main commuter runs 700x35 tires, my old road bike 700x28, and my old mountain bike commuter 26x1.85 smoothies in the summer and 1.65 sutdded snow tires with aggresive tread in the winter.
Used to get 1-2 flats a month. (Freaking goat-head thorns). Started using tire liners (Mr. Tuffy's). Now maybe 1-2 flats a year.

People on bikeforums generally don't care for tire liners, but they work for me. I've tried heavier, more puncture-resistant tires and they tend to not have supple sidewalls, which is what I prefer.

I suppose the newest way to deal with punctures is to go tubeless and use (and maintain) the sealer-goo that one squirts inside them. It seems to work for most who do it.