It is not by accident that this is the very first question that we decided to answer on Ask Dumb Runner. In our experience, it is possibly the single most common question you hear from beginners. Even longtime runners can spend a lot of time and energy trying to find the "best" shoe.
Usually, they overthink it.
As described on our Gear FAQ page, choosing running shoes is actually pretty simple. (Really.) To quote ourselves, it's a three-step process:
Visit a specialty running store. Not the "athletic shoe" emporium at the mall, with the window display of Nike high-tops. A real running store. One that sells running stuff only and is staffed by actual runners.
Tell them a bit about yourself – your athletic and/or running history, if any; your running goals; and anything else you feel might be pertinent (injury history, foot problems, etc.).
With their help, try a few pairs of shoes. Run a bit in them. Buy the ones that feel the most comfortable to you.
And that's it.
If anyone instructs you to buy a certain brand of shoe—ASICS or Brooks or Nike or whatever—smile politely, nod, and change the subject. That person surely means well, but there is no such thing as The One Best Running Shoe or even The One Best Running Shoe Company. No single brand is empirically "better" than another. There's just too much individuality and subjectiveness at play when it comes to choosing running shoes.
In short: The best running shoe for you is the one that you (literally) feel is the best running shoe for you. Period.
If you feel overwhelmed by the choices out there, RunnersWorld.com has a handy Shoe Finder tool that can help you narrow them down, suggesting shoes based on your answers to several questions about things like weight, current running mileage, history of injury, and so on. Runner's World also publishes excellent Shoe Guides several times a year, reviewing many of the newest models. [Disclosure: I am a writer at large and columnist for Runner's World.]
Oh, and by the way: It is perfectly natural to want shoes that look cool. Just don't let cosmetics dictate which shoes you choose. When it comes to running shoes, it is definitely not better to look good than to feel good.