I may have to write a hub on this! My tip would be to see a professional at a specialty shoe store and have them videotape you on a treadmill to watch your gait. Some people are going to the minimalist running shoes, or even barefoot, on the basis that it is more natural and you get less heel strike than with a padded shoe with lots of support.
Choosing a good pair of running shoes depends on several factors such as: (1) beginner or experience; (2) trail or road running; (3) distance you run each week; and (4) whether weight of the shoe or support is necessary/important to you.
I've been running for years and always replace my running shoes with the same brand/style. It works for me! :)