Once perfected, this trick can definitely impress your friends. It can also help you win bets like "So, if I can open my beer using only your $20 bill, do I get to keep it?"

[edit] Steps

Fold the dollar bill in half.
Roll up the dollar bill as tightly as you possibly can.
This is what your dollar bill should look like.

Bend the rolled dollar bill in half to maximize the pressure at the bend.
Put it on top of your bent index finger and hold it tightly in place with your thumb, with the bent part sticking out.
Grab the bottle around its neck and push the cap upwards with the bend in the dollar bill until it pops off.

[edit] Tips

It takes a lot of practice and reasonable arm strength to perform this trick.
It helps if you use the hand you're holding the bottle with to get leverage by using it as a fulcrum.
First learn to do this with another bottle, then you'll understand how to use a dollar bill. It's all about using the object as a lever.
A lighter can also be used in same way.
Damaging the bill is only a crime in the United States if done "with intent to render [it] unfit to be reissued." ^[1]

[edit] Warnings

Take care you don't rake your fingers across the edge of the bottle cap. The cap is sharp and you WILL get a deep cut.
Make sure you don't hit your eyes or anyone else's when the cap pops off.
Don't shake the bottle before opening it.
Drink responsibly.
Be careful not to break the bottle in your hand
Special Note: Coronas are notorious for popping loudly and the bottle cap will shoot off like a champagne cork. Which is cool, as long as you're not aiming it at anyone. Heinekens have also been known to do this.