Glass and glassware

When you go to a bar, you will the bartenders give each person a different type of glassware with their cocktail. The reasons for doing this are plentiful. The main factor is that some drinks have ice in them while others don't. A cup with a stem is used to prevent contact between the hand and drink so the cocktail can stay chilled for a longer period of time. There are also cups designed to enhance the flavor of the drink while others are used to serve drinks with certain volume or even for aesthetics.
Highball Glass
This piece of glassware is used to serve cocktails which have two main ingredients, an alcoholic spirit and a mixer liquid. These drinks are always served with ice. The long, wide, and straight dimensions allow the bartender to fill up to 12 ounces.

Cocktail Glass
The Cocktail Glass is used often to make create martinis and for that reason is also known as the Martini Glass. With a stem for elegant drinking, the V-Shape shape holds up to 6 ounces.

Old Fashioned Glass
A short and think cup which is also known as the Lowball Glass, this piece of glassware is used to create the simplest of drinks. Usually served with ice, these drinks include popular Jin  amp; Tonic or a Scotch on the Rocks.

Wine Glass
These glasses are designed to hold the aromas of the drink within the cup, usually for wine. They come in different sizes, from 6-10 ounces and are designed to be elegant while useful.

Champagne Flute
Named after its design for the drinking of champagne, serving drinks in this glass will help preserve the carbonation due to less surface area being exposed. The tall and slender design shows off the bubbling within champagne beautifully.

Shot Glass
A small piece of glassware designed to take shots with. Holding 2 ounces of liquid, these drinks are served with no ice and are intended to be finished in one shot, hence the name.

Collins Glass
Usually used to serve drinks which are intended to be cool and refreshing. Holding 10 or more ounces of liquids, this cup is most known for serving the Tom Collins or recently, many summer drinks.

Sources:
Hess, Robert. "The Essential Bartender's Pocket Guide"
SuperCocktails.com