The correct plural form of the drink gin and tonic, as far as I'm concerned. Other forms you may come across include:
Gin and tonics: This is quite common, and results from the treatment of "gin and tonic" as an indivisible unit, or some sort of German-style compound word. There is an argument to be made that "gin and tonic" is the proper name of a particular drink, and thus indivisible. However, as "gin and tonic" is not capitalised, I do not believe it could be said to be a proper name. Asking for "3 gin and tonics", therefore, is nonsensical: you are asking for "3 gin", which means nothing, and an unspecified number of tonics.
Gins and tonics: This is less common, but no more acceptable than the above. Pluralising both words leads to an ambiguity: are we referring here to a number of gins and a number of (separate) tonics?
"Gins and tonic", then, is your only man. Asking for "3 gins and tonic" clearly indicates that you want 3 glasses of gin, and you wish them each to be served with tonic. (The ice and lemon are understood in this context.)
If you still don't believe me, you might ask yourself how you would order more than one vodka and tonic.