The Martini FAQ goes above and beyond the call of duty.
A highly vocal minority of Martini drinkers, the Prescriptivists,1 insists that the short answer is in fact the only answer. Any deviation from this definition may produce an enjoyable cocktail, but it will not be a Martini. (There is a single exception: one may use less vermouth.)
Strict adherence to the Prescriptivist position brings with it several undeniable benefits. Foremost among these is the quality of the drink itself: it is difficult, perhaps impossible, to truly improve on the classic American Dry Martini. There are also practical benefits, since the Prescriptivist has no need to stock an elaborate bar. Give him an ample supply of the two base ingredients and a fresh stock of garnishes, and he's set. Finally, there is the bracing sense of keeping the barbarian at the gate, of shielding a flickering flame of culture against the gusts of fad and fashion.
Yes, you're reading that right. It has footnotes.
And yes, of course I'm a Prescriptivist. Vermouth. More gin than vermouth. Chilled. Twist or olive. Cocktail glass. Straight up. Cocktail glass. That's it.
If you add apple-flavored goo, it's now an Apple Cocktail.