If you don't know the difference between a hurricane glass and a zombie glass, there's still hope for you. Get your head out of the oven and refer to this handy list. I expect you to have a full complement of each of these types of glassware.

I shall not waste my days in trying to prolong them.
Ian L. Fleming (1908-1964)
Cocktail
Let's clear up this misconception right off the bat: this is called a cocktail glass. It only becomes a martini glass when it contains a mixture of vermouth and either gin or vodka. Say it with me: "cocktail glass."
Hurricane
For serving hurricanes or other large fruity drinks. Usually calls for an umbrella. Looks like a very tall daiquiri glass.
Daiquiri
In addition to daiquiris, a good all-purpose fruity drink glass. Looks like a short hurricane glass. Give it an umbrella, a fruit wedge and a bendy straw.
Margarita
You've seen these at Chevy's, right? Well, they have margaritas in them.
Zombie
This is just a tall, very skinny cylinder. The skinnier the better. Comes in frosted and non-frosted glass.
Double Old Fashioned
The all-purpose glass for non-fruity drinks. Comes in a variety of styles, but they're all about three to four inches in height and diameter.
Shot
It's a shot glass. If this needs explaining, maybe you'd prefer this site.
Cordial
(Not to scale) Looks like a very tiny champagne glass. Comes in a variety of styles. Used for cordials, such as Chambord & Cream.