Feet come in all different sizes and shapes and therefore have different biomechanical properties.  These different biomechanical properties mean your feet are unique and need the right type of shoe to accomodate them.  Originally, man's feet were designed to walk on the earth and accomodate to the surfaces they were walking on.  However, as the surfaces we walk across have changed and societal norms have expected us to wear shoe, it is important that the shoe fit the needs of the foot.

Feet generally fall into one of three categories: over-pronation, neutral, and under-pronation (also sometimes called supination).  Ideally, we would all like to fall into the neutral category, but we don't so sometimes we rely on our shoe to help keep us in a more neutral position.  Now this may sound really high tech, but determining your foot type is relatively easy.

Take the Wet Test:
 

To take the Wet Test, dunk your foot in water and then stand on any surface that will leave an imprint of your foot.  When you look at this imprint, you should find that you have one of the three most common foot types described below. While not every foot completely mimics these three types, you can  still use the Wet Test to determine your general foot type      and select the shoe shape most appropriate for your foot.

TheNormal Foot has a normal-sized arch and leaves an imprint that shows the forefoot and heel connected by a wide band.  A normal foot lands on the outside of the heel, then rolls inward (pronates) slightly to absorb shock.  Runners with a normal foot and normal weight are usually considered biomechanically efficient.

The Flat Foot has a low arch and leaves a nearly complete imprint. That is, the imprint looks like the whole sole of the foot.  A flat foot usually indicates an overpronated foot that strikes on the outside of the heel and rolls inward (pronates) excessively.  This type of foot is a tremendous shock absorber, but because of this is prone to overuse injuries.

The High-Arched Foot is the one on the far right.  These feet leave an imprint showing a very narrow band connecting the forefoot and heel and are generally termed a supinated or underpronated foot (the terms are synonymous). This type of foot doesn't pronate enough, so it's not an effective shock absorber and is also prone to overuse injuries.
 

Have somebody watch you walk
Or you might be able to watch yourself in a mirror.  What you want them to look for is if your foot rolls in excessively (pronation) or doesn't roll in enough (supination) during the weight bearing phase of gait.  Also watch for feet turning out (like a duck), this usually leads to excessive pronation.  People that walk "up on their toes" usually have tight calf muscles and need to stretch them out to prevent injuries.
 

Look at the wear pattern on the bottom of an old pair of shoes
 
 

Normal wear pattern on the bottom of a shoe should mimick the force distribution pattern seen to the right.  Shoe wear along the ouside boarder at the heel is normal.  If the heel of your shoes is worn on the inside (relative to the outside) you over pronate.  Additionally, if the wear pattern shows only wear on the outside edge, you don't pronate enough.  Remember, your shoe soles should be worn in a pattern similar to the orange dot.