The elegant champagne bottle handles pressures of 70-90 pounds-per-square-inch, while the plain old average car tire handles only around 30 psi. Why keep champagne at pressures that would pop a tire?
Champagne's delightful fizz is due to simple carbon dioxide bubbles that are produced as grape juice ferments into alcoholic wine. Before the bottle is opened, this carbon dioxide is mostly dissolved in the liquid, with only a little pocket of gas just beneath the cork. This is where pressure becomes important. The amount of gas dissolved in the champagne is proportional to the pressure: so, if you want a lot of bubbles (and who doesn't), you must keep the carbon dioxide gas under a lot of pressure.
The champagne bottle has several mechanisms designed to handle high pressure. For example, that wire cage on the cork does more than look pretty. It keeps the carbon dioxide from launching the cork right into your eyes or into your chandelier. Also, the glass bottle is thicker than a regular wine bottle, and many claim that the punt or the dent in the bottom adds strength.
There are several things you can do to help champagne remain pleasantly fizzy and to prevent any unfortunate explosions. Chilling the bottle reduces pressure by keeping the carbon dioxide dissolved. Handling the bottle gently is also a good idea: given the high pressure inside, it's not only sensible but looks rather debonair.