Generally, you want to run the MAXIMUM presure on the sidewall, unless there is a good reason not to. The reasons for this are:
This gives you the maximum load-bearing weight of the tire - remember, as you turn, accelerate, and brake, the load on each individual tire changes. Being at max gives you more wiggle room to prevent a blowout due to an extreme dynamic load condition.
The tire will run cooler, with less sidewall flex, making it less prone to blowout and increasing life of the tire.
Maintains the pressure on the ground of the center of the contact patch.
Best gas mileage.
Reasons NOT to run max pressure are:
Ride comfort.
The axle the tire is on is lightly loaded, and max pressure prevents the inner and outer edges of the contact patch from putting full pressur on the ground, causing traction, handling, and tire wear issues.
An attempt to adjust understeer/oversteer characteristics of the vehicle with differential pressure.
Different brand/construction of tires on different axles.
Best way to tell if you are over or under inflating that is available to normal people is a chalk test. Take a crayon or piece of chalk, and mark the trad of each tirefrom a couple of inches in from the outer edge to a couple of inches up the outer sidewall, a couple of inches wide. Drive a few blocks, including turns in both directions, and stop and look at the markings:
If the markings are worn off right where the tread stops and the sidewall begns, the inflation is good for those load conditions.
If the chalk extends past the sidewall and onto part of the outer edge of the tread, the tire is overinflated for those conditions.
If the markings are erased accross all of the tread, and partially up the sidewall, the tire is underinflated.
Remember - all pressures are COLD - bumo them up 2 lbs per 35 pounds of pressure if the tires are hot.