What is the best brand for running shoes ? Asics, Nike, Puma?

To answer your question as far as which brand is best, it really just depends on your foot type and the amount of running you are going to be doing. All it comes down to in the end, is if the shoes work for you. The difference between $60 Asics and $120 Asics usually is the quality of the shoe. While the shoes may look very similar, running shoe companies make high-quailty shoes for serious runners who are willing to pay the price and lower quailty shoes for average shoe buyers. If you look at the two shoes, you will usually see a difference in the soles of the shoe and the in-step. To answer your last question, it is good to have running shoes because they are built for the impact and fatigue that comes with pounding the pavement. Ordinary shoes usually aren't built for the amount of impact that people put on running shoes. I think you also may want to consider Saucony, Brooks, and Mizuno shoes. I would recommend you go to a specialty running store like Runners Roost or Road Runner, or whatever store you have in your area and the sales people can answer all your questions and fit you with a shoe that is correct for your foot. When you are at the store and being helped as well, remember just because a shoe is more expensive, doesn't mean it is better; buy the shoes that feel the best on your feet.