The Sling

Mixing drinks is a very, very old practice, but it wasn't until the mid 19th century that these mixtures started to resemble what we call "cocktails" today. In fact, a "Cock Tail" was a kind of mixed drink at the time, containing just a spirit, water, sugar, and bitters (which today is called an "Old-Fashioned," referring to serving a cocktail the "old-fashioned way"). Going back further there are the Toddy, the Julep, the Sangaree, and the Sling, all of which were almost exactly the same thing, leading to some confusion down the line.
(I am of course avoiding Punches here, which are even older and range from just as simple to much more complicated. The Sour and the Fizz and the Collins, etc, are all descendents of Punch).

A "Cock Tail," in its original definition, was first referred to as a "Bittered Sling." Let's back up and look specifically at the Sling.

The definitive knowledge on these 19th century drinks is from the grandfather of bartending, Jerry Thomas. He wrote the first tome on bartending and mixed drinks in 1862, which included a collection of Punches as well as each of the above mentioned cock-tail precursors. The Toddy and The Sling (likely named after "slinging one back") are essentially separated only by temperature - a Toddy was usually served hot, and a Sling was usually served cold (though you could get a Cold Toddy and a Hot Sling, so again - confusion). In his first book he including a scrape or two of nutmeg over the Sling, while the Toddy was without, but in the second edition in 1887 removed this distinction. The Gin Sling, dating to about 1800, became a staple in American drinking, even commonly being consumed first thing in the morning. As always, alcoholic mixtures were considered medicinal, but it quickly surpassed this use and became wildly popular in every corner of the country. Adding further to its popularity was the increased availability of ice around the 1830's, making cold drinks more common, and drinking in general a little more accessible (room temperature drinks are definitely not as palatable).

Gin was the most popular of Slings, but you can of course use any spirit (Cognac and rye would have been common as well). At the time, Holland-style gin would have been the kind used, and not London Dry like we're used to today. It's hard to find, though David Wondrich offers a very simple suggestion to recreate it in his fantastic and inspiring book (from which I am getting much of the information in this post) - simply mix 60% Plymouth gin with 40% Irish Whiskey. (Irish Whiskey and Holland gin / genever are actually related and have taste similarities). He does also offer another suggestion in that spirits back than were typically higher proof, and thus a Sling required a little more water than nowadays. Decreases the 1oz to 0.5oz is a good idea if you're using an 80-proof.

Here is the recipe from Jerry Thomas' first edition for the original Sling:

2oz of spirits
1oz of water
1 teaspoonful of powdered white sugar (which equates to about 1/2oz of 1:1 simple syrup)
1 small lump of ice

Stir with a spoon.
[Grate some nutmeg over top]

In the 1862, Queen Victoria's Chef, Charles Elme Francatelli, published his own book including a very different Sling using juice and some liqueur, which by 1915 had spawned the Singapore Sling, using
Gin
Cheery Heering
Cointreau
Benedictine
Grenadine
Pineapple
Lemon
and Angostura bitters. 

Quite the change. Its popularity unfortunately brought the demise of the traditional Sling, and now if you order a Gin Sling you will typically receive the following:
Gin
Sweet vermouth
Lemon juice
Sugar
Angostura bitters
Soda

Just like most classic drinks, including the Cock Tail, variations and creativity were the death of tradition. Of course, without variation, we'd have nothing we do today - including even the Cock Tail itself, which as I mentioned is simply a Bittered Sling.