Believe it or not...

When I worked at a Steak & Ale restaurant, the manager there successfully opened a bottle of cheap white wine following these steps:
  1. Remove foil covering the cork.
  2. Fold a cloth napkin in half and half again, and wrap it around the base of the wine bottle.
  3. Find a firm, wooden, flat vertical surface, such as the jamb of an open doorway, or maybe a very solid wood wall.
  4. Stand facing the hard surface and hold the wine bottle above one shoulder with both hands. One hand should be on the neck of the bottle, the other hand near the base holding the napkin on.
  5. Pound the base of the bottle into the wood surface repeatedly, being sure the base of the bottle strikes the wood evenly (through the napkin's padding).
  6. The inertial sloshing of the wine in the bottle will slowly push the cork out, assuming the cork isn't old and rotting.
A few downsides: the wine will be very fizzy for about 2 hours afterwards, assuming you haven't spilled it all over the floor; the wood surface may be damaged; you will be perspiring heavily; the risk of injury to yourself and spectators is nonnegligible. Try this at your own risk!

Perhaps this technique is not so great for opening wine bottles, as it is for opening wallets: the restaurant manager made $5 in wagers off of each of 6 or 7 waiters.