This is the easiest question of the day.
Check out what Fred Hatfield had to say:
http://www.sportsci.org/traintech/strengthshoes/fch.htm
Here's his overview:
Summary. A recent study found similar small gains (~1%) in sprint and jump performance when previously untrained young men trained for 10 weeks in regular shoes or Strength Shoes. Injury rate was much higher with Strength Shoes, probably a result of the inappropriate training program prescribed by the manufacturer. An earlier study of more experienced athletes showed trends towards better performance and less injury with normal shoes. I therefore cannot recommend Strength Shoes.
The study he cites is from 1996, but if there's more recent information validating these things, I sure haven't seen it. Strength shoes are sort of like chromium picolinate--no evidence they work, but lots of devoted fans.
Not to mention a great Seinfeld episode ...