Everyone needs to wear running shoes that are meant for TRAINING not RACING.  The best shoes will have a wide, supportive heel cup and cannot be easily bent in half at the middle.  Those shoes are racing flats and they do not provide proper support for the impact your legs, feet, and joints will receive while training.  

Suggestions - Please do not feel that you must purchase one of these styles!  Do some research - I also suggest going to a running store such as Miles Ahead Sports in Wall or Runners High in Freehold.  They should help you find the perfect shoe for your foot.  However, please be sure to ask for training (or even trail) shoes and NOT Racing flats.  In the past I have suggested the following shoes - however these are just suggestions - there may be newer models of these shoes or more current choices.

New Balance 840

Adidas Supernova Riot

Asics GEL-Trabuco 11 WR

Saucony ProGrid Xodus

Salomon Speedcross 4

Asics Gel Kayano 24