Running Shoes vs. Weightlifting Shoes

There is the right tool for the job. You wouldn't try to pound a nail in with a screw driver. You might eventually get it in, but a hammer would have been much more efficient. Similarly you shouldn't expect to come into the gym in your normal running shoes and squat as efficient as you could with weightlifting shoes. This video does a good job of showing the difference between the two.

Here are some links to places to buy different weightlifting shoes:
Pendlay Barbell Do-Wins
Rogue Fitness Weightlifting Shoes
Adidas Weightlifting Shoes