What cocktails can I make with just gin and vermouth?

Gin and dry vermouth make a classic Martini; gin and sweet vermouth make a Martinez or a Gin and It. Both are stirred and served up.

If you have only gin and dry vermouth, you can make a Martini (2 oz gin, 0.5 to 1 oz dry vermouth, stirred, lemon twist or olive). If you have sweet vermouth instead, you can make a Martinez (gin, sweet vermouth, a dash of maraschino, orange bitters) or its predecessor the Gin and It (equal parts gin and sweet vermouth, no ice, no garnish — a pre-Prohibition style still served in some Italian bars). Add a single bottle of bitters and the range widens significantly: a Hanky Panky needs only gin, sweet vermouth, and Fernet-Branca. Add Campari and you have the Negroni. The 2-bottle constraint is more permissive than it sounds — gin and vermouth is the foundation of an entire pre-Prohibition cocktail vocabulary.