The leading cause of tire failure is underinflation.  Improper inflation can cause decreased performance, lower gas mileage, reduced grip, exacerbated wear, and in dire cases, tire failure.  Tire pressure should be checked manually once a month at the absolute minimum, though it is best to do it weekly.  We recommended that you do so during the cooler morning hours, and before emarking on a drive any longer than a mile.  Ambient and frictional heat can muddle pressure readings.
 
Over time, tires tend to passively leak air through a process called permeation.  On average, a tire will lose about 1 psi per month during the colder months, and even more during spring and summer.  Also bear in mind that a 10° F drop in external temperature lowers pressure by about 1 psi.
 
Also beware of overinflation.  Too much tire pressure can be just as harmful as too little, leading to excessive tread wear and and an increased risk of blowout.

Be mindful of your tires' condition and regularly examine them.  A tire is worn out and should be replaced when the tread depth is reduced to 1/8 in.  Check for cracks, cuts, and other irregularities in the sidewall or tread, which are strong indicators of a tire on its way out.  Also be on the lookout for uneven treadwear, which usually indicates poor wheel alignment or worn suspension components.  When purchasing new tires, have your alignment and suspension checked to prevent them wearing prematurely.

Because of the uneven duress and wear of each wheel position, it is necessary to have your tires rotated to maximize their lifespan.  Unless the manufacturer specifies otherwise, we recommended a 5,000 - 7,000 mile interval between rotations.  Though regular rotation extends tread life, it will not cure damage caused by other factors.  If a tire is showing uneven tread wear or if the wear bar is showing through, the only remedy is replacement.