Ours is a three-part solution:
1. Denial - In this phase we struggle futilely with the cap, convinced that one more rallied effort to unscrew the lid will avoid any further work on our part.
2. Apply Hot Water - Once we've accepted the inevitable, our next trick is to run the lid under warm water. We're not entirely sure of the science involved, but we think that the hot water helps expand the metal cap (loosening its grip) and also warm whatever sticky substance is preventing the cap from turning.
3. Further Struggle - If we don't already have it out, we reach for our jar opener of choice. We dry the bottle off, take a deep breath, and give the cap a good, firm twist. Making a face and grunting also seems to help.
Most of the time, this seems to do the trick. If not, we repeat these three steps until we either succeed or give up and use a different condiment instead.
A final step would be to actually clean the cap and the threads of the bottle to avoid the whole situation next time, which we will grudgingly do about half the time. A dish cloth dampened with warm water works for this and a second towel works to dry things off again.
What's your sticky bottle-opening strategy?