• Walking - Casual use ($45 - 80)
• Running - Extra cushioning, support and durability. ($100-$130)
  Trail Runners -
    Rough terrain - Thicker soles, Deep treads, heavier.
    Trail shoes - usually have a wide and low profile so the foot is closer to the ground for more stability on irregular surfaces.
    See: Important Trail Running Shoe Features
• Cross-trainers - Compromise between walking and tennis or other court shoes.
• Sport Specific -
  Basketball ($60-$140)
  Tennis ($75-$120)
  Soccer
  Golf
  ...

It is recommended that you replace running shoes between 350-550 miles depending on your running style, body weight, and the surface on which you run.
A shoe's midsole cushioning may be worn out long before the tread shows signs of wear.

See feet under health to determine whether your feet over pronate (roll inward) excessively or underpronate (supinate).

• Motion-control shoes are better for moderate to severe over pronators, they have extra support on the medial (arch) side of their shoes. You may be able to replace your insoles with third party insoles/orthotics to provide medial support.
  See feet under health.
  Google search
• Stability shoes are better for normal pronators and moderate overpronators. These shoes have some medial support and good midsole cushioning. Because normal or medium arches are the most common foot type, most runners will need Stability shoes.
  
• Cushioning (normal) shoes are better for normal pronation and supinators (high arch). These shoes do not have medial supports but are more concerned with midsole cushioning.
  Normal pronation (rotation of up to 15%) provides some natural cushioning, underpronators need more cushioning to compensate.
  Google Search

Asics, Brooks, New Balance and Nike are popular brands.

March 2010 Runners World reviewed shoes
They the Brooks Glycerin ($130) an editors choice.
New Balance 760 for durable but soft cushioning if you have excessive heal wear.
Adidas Supernova Glide 2 for supinators.
Asics Gel-Kayano (a stability shoe) for overpronators.

A specialized running store is better than someplace like foot-locker. A good store will analyze your gate by watching you run or with a machine and provide custom advice on fit.
Run (foot-locker's running store) had tread mills with video cameras which can take slow motion video of your gate.
See: Specialty Running Stores at RunnersWorld.
run.footlocker.com

Links:
Foot problems (pronation explained)
Shoe Types @ runtex.com
Find the Right Running Shoe - DukeHealth.org
Best Shoe Choices for Walking or Running
Athletic shoe guide from Consumer Reports
When to Replace Running Shoes
Running Shoe Reviews at RunnersWorld.com