Trick: Push the cork all the way into an empty wine bottle. Bet your mark that you can get the cork out without breaking it or the bottle.

Solution: Take a cloth napkin and carefully push one of it's corners into the bottle so that it makes a channel for the cork. Keep feeding the napkin into the bottle until it extends past the neck enough for the cork to fit in the channel. Shake, tap or move the bottle in a way that it causes the cork to land in the channel the long way. Slowly pull the napkin out of the bottle bringing the cork with it. It's going to take some strength but it will come out just fine. Just make sure that no one is too close or you may hit them with your arm or the cork when it finally pops out.

Here's a video of another version of this trick.