The first and best way to ensure a healthy lawn is to cut it high.
As mentioned on the mowing techniques page which is worthy of repetition, "When you mow, you prevent seeds from generating and so your lawn, in turn, produces more sprouts frantically trying to find a way to regenerate."
Mowing too short is the number one offense reported by the lawn patrol. Just like with trees, the height of the top relates to the depth of it's roots. Grass with deep roots has a better chance to survive a drought and it also keeps the soil shady, preventing moisture loss and drying of the sun, which in turn, compacts the soil. A taller grass blade absorbs more light, has more nutrient producing cells, and it resistant to invading weeds.
For suggested blade heights for different types of grass see the mowing chart for your ideal lawn height.