Purists attend to the so-called fact that the original or "template" martini has gin and vermouth as its base. However, the martini of choice today, albeit a choice, leans more towards vodka.
What's usually meant by a martini consists of two ounces of gin or vodka and a quarter ounce of dry French vermouth. The liquor is poured into a shaker filled to the brim with ice, shaken vigorously, and strained into a martini glass.
But wait! No cocktail can call itself a "Cocktail" without the addition of a garnish. Perhaps the most well-known garnish is the pimento-stuffed green olive, skewed by a toothpick and placed lovingly in the glass. Another common garnish is the old twist of lemon, which is more of a sliver than a twist.
Personal preference certainly plays a role when choosing a garnish, as it does in picking a perfect martini. As with any recipe, certain flavors work better together. A crantini for example (Cranberry Juice, vodka and dry vermouth) has a few cranberries swimming around, while the Gibson's pickled onion is at the other end of garnish flavor.
Of course you have to take into account the various deviations and ingenious creations put forth by bartenders across the globe. The olive is still prevalent, but can now be found stuffed with blue cheese or anchovy paste, while pickled asparagus and miniature eggplant are favorites in cosmopolitan circles. Maybe a caper suits your fancy, or a thin slice of cucumber; how about a red-hot jalepeno?
As you can see, there are no limits to what can garnish a martini - or recipes for that matter. What is important is to make sure the tastes go together, and of course this demands testing.
There are worse jobs than testing martinis.