To follow up on all that information about absinthe, I found another drink that includes the infamous green-tinted libation. And this cocktail, though you may not have heard of it, is so popular and critical to American culture that it's the official cocktail of Louisiana.
It's the Sazerac, one of the oldest cocktails around. And it's defining feature is that it includes absinthe in the preparation -- not in the drink itself, but serving the same purpose that vermouth does in a martini. I've included the recipe for nightlifers (from cocktails.about.com) on how to concoct a Sazerac. You can also see a live video on how to make it here.
3 oz rye whiskey
3/4 oz simple syrup
Peychaud bitters to taste
absinthe or absinthe substitute
lemon twist for garnish
Chill an old-fashioned glass by filling it with ice and letting it sit while preparing the rest of the drink. In a separate mixing glass, muddle the simple syrup and Peychaud bitters together. Add the rye whiskey and ice to the bitters mixture and stir. Discard the ice in the chilled glass and rinse it with absinthe (or substitute) by pouring a small amount into the glass, swirling it around and discarding the liquid. Fill the rinsed glass with crushed ice. Strain the whiskey mixture from the mixing glass into the old fashioned glass.
Garnish with a lemon twist. Traditionalists will say that the lemon twist should be squeezed over the drink to release its essences but that the twist should not be dropped into the glass itself.