If I have to pick one drink to take to a desert island, it's the classic Sazerac.
That is what I will want most of the time when I want a cocktail. However, I will allow a few others to enter rotation, depending on mood, time/temperature, and place:
Margarita.
Vesper.
Pastis.
And, finally, my embarrassing guilty pleasure (which I never order except when I am in company I know well or I am on a Caribbean island): piña colada.