Vermouth's most famous
moment is as the lesser part of a
martini (esp.
gin martini). The portion of vermouth defines how wet the martini is, and most people prefer dryer martinis.
It has been noted that an ideal gin martini is a glass of gin
drunk whilst looking at a picture of vermouth.
Along similar lines, during one of the early
atomic bomb tests, a bottle of vermouth was strapped to the device so that in the future, all one need do to make a perfect dry martini would be to
hoist a glass of gin to the sky. Bear in mind that the authenticity of this anecdote is in
doubt, as I can't remember where I read it.
Vermouth's second most famous use is simply as a
cooking wine.