Vermouth is not gross or evil. This tip should not serve to scare you. Lower that eyebrow, ease that scowl. People (Americans) are afraid of vermouth – David Wondrich likes to say that bartenders treat vermouth like toxic waste. I understand. I felt the same way.
First!!! Throw away your old dusty bottles. Crack into a new, chilled bottle and pour yourself a thimble full. Taste it fresh. Taste a variety of vermouths. Most importantly, every time you reach for vermouth to make a cocktail, taste it to make sure it is fresh. Vermouths (sweet, dry or bianco) all taste pretty good, and if you can’t stomach it neat then you should not put it in a cocktail.
Second!!! Refrigerate, seal, preserve, and care for your vermouth (it goes bad). Think of it as wine, because it is. So keep it fresh, cold and buy small bottles so you can use it up faster. Also, you can use it for cooking in place of white wine.
For more about vermouth, read this article from the San Francisco Gate.