Cocktail glasses come in all sizes and shapes. What you decide to put in them should determine the glass you use. There is a logic to the design of each glass that is intended to enhance the flavors of the different cocktails.
The logic in the coupe revolves around the ingredients. Most cocktails—simple or complex—fall into the categories of martinis/Manhattans, sours, and old fashioned's. Of these, Manhattan-style cocktails and sours both have enough extra stuff going on (vermouth, additional modifiers like bitters and liqueurs, sugar, and/or citrus) that they’re naturally not too boozy.
Cocktails, properly mixed by someone who knows what they’re doing, come to you balanced, perfectly diluted, and cold as hell. The mixer has carefully added the correct amount of water by shaking or stirring, so you don’t want to mess that up with extra ice, or warm it up by getting your grubby hands all over it, which is where the stem comes in.
Generally speaking, you also want a coupe that is a bit larger than the total volume of your drink. This prevents spillage, and also aids in harnessing aromatics, be they naturally occurring in your chosen spirits.
While most cocktails shouldn’t require extra dilution after mixing, some cocktails, particularly old fashioned-style beverages, benefit from it greatly. By “old fashioned-style,” we mean cocktails that follow a template of spirit, sweetener, modifier, and water. Most commonly this means whiskey, sugar (or sugar syrup), bitters, and ice, but it can just as easily mean any barrel-aged spirit—rum, tequila, barrel-aged gin.
Similarly, some sours—punches, tiki drinks, etc.—need a little extra water because their ingredients may otherwise be overly sweet, viscous, boozy, or otherwise unpleasant. In all of these cases, you’ll want to tailor the type of ice you use to your desired level of additional dilution. The point is these drinks need ice, and a double rocks glass can hold all that ice.
Collins glasses serve the same function as champagne flutes - they're longer and taller to get maximum effervescence out of whatever fizzy ingredients you're adding. They tend to be a little bigger volume-wise, to accommodate the 1 1/2 -to- 2 ounces of additional liquid.
Anything else, glass-wise, is probably non-essential, though glassware trends, like any others, still oscillate wildly. Stemmed wine-glasses are currently en-vogue for all manner of sours, collins, and spritzes, as are chunks of ice floating in oversized coupes. Manhattans can be served up in a rocks glass, and Sazeracs perennially defy all manner of convention.
Lifehacker provides a good detailed discussion on each of the glasses discussed above.