Tire pressure can effect things like tread wear, mileage, ride quality, etc. There are several schools of thought re: tire pressure, including but not limited to:
1) Inflating to to manufacturer recommended tire pressure (typically 25-35 psi, depending on the car - it's on that sticker inside your door). Generally, this is recommended if you have OE or OEM-spec equipment, since the manufacturer recommendation is supposed to get you approximately the mix of handling, mileage, ride quality, etc., that you bought the car for in the first place, and takes the mass of the car into account.
2) Inflating to 80% of the maximum pressure written on the sidewall of the tire. (e.g. 40psi for a 50psi max tire) Generally, this is recommended for aftermarket tire/wheel combos, different sizes that what originally shipped with the car, etc. It's a safe middle-of-the-road thing to do when the manufacturer recommendations no longer apply. But you would want to monitor tread wear, ride quality, etc., and adjust up or down as needed, since both over-inflated and under-inflated tires cause problems.
3) Inflating to the needs of the situation. This could include lowering psi for offroading, adjusting to compensate for weather conditions, or adding 5-10 psi before storing a car to avoid forming a flat spot on the tire when it's parked. Basically you need to be the sort of nerd who carries around an air gauge and a compressor in their trunk, but some people do this.
4) Inflating to sidewall - inflating to the max pressure listed on the sidewall of the tire. I have never seen this advocated outside of ATOT, I think it's more of an in joke than actual advice. You can read the old troll thread and see what the justification is.
For a perspective on this:
http://www.popularmechanics.com/cars/a940/4199963/