A cocktail glass looks elegant.
Must be something about that thin delicate stem.
It's the right kind of glass for showing off.
You can just picture it:

Jake and Brett sipping their martinis off the bar until they're drained enough to pick up.

That rich lawyer talking over Manhattans at a corner table, the brass and curtains behind him gleaming and velvety.

That college girl sitting in the comfy chair sipping an absinthe cocktail and dreamily, amusedly watching the crowd of party-goers.

Remember, kids: If you drink gin out of a tin cup, you're a drunk, but if you drink it out of a cocktail glass, you're James Bond.

Of course, ultimately the shape of the cocktail glass is utilitarian in nature: it keeps your cold drink away from your hot little fingers.