Em's writeup is the last word, but I am tempted enough to pass a bit of secondhand experience into the apocrypha of the martini.

A friend of mine frequents a martinitorium in San Francisco that he swears by. The short old bartender comes over to the table with a pushcart to mix each round. My friend says once he asked the bartender what his (the bartender's) secret was. "Sometimes I forget the vermouth" came the reply with a shake of his wizened old head.

There are all kinds of sophisticated martini variants, drinks based on the martini, not just substitutions for gin or vermouth. And then there are the drinks that are named after the eponymous "Y"-shaped glass in which they are served. Here are a few to start:

Please /msg me with other martini variants that have been properly imbibed by E2 so I can keep this list up to date.