Inflate Your Tires

Frequently

By far, the most common flat that bike shops repair is a "pinch flat". Its cause is under-inflation resulting in the tire compressing all the way to the rim, with the tube trapped in between. Removed from the wheel, the tube will have a tell-tale snakebite puncture --> : <-- just like that punctuation, two small holes vertically adjacent.

Below ~25 mph, the dominant force you pedal against is rolling resistance which is mitigated primarily with air pressure. Too much pressure will result in your horizontal path through space having a greater vertical amplitude, increasing the actual distance traveled. 

Unless you only ride on polished velodrome surfaces, the aim of inflation is not maximum pressure - it is correct pressure. Whatever you discover it to be, that pressure will be different tomorrow. For very light weight rubber, it will be significantly less at the end of today.

The ultimate solution to pinch flats is to not have anything to pinch - go tubeless.