Lime juice's magic lies in its ability to make almost any clear alcoholic beverage decidedly more palatable. When used in the right proportion, its sour but distinctive flavor can cover even the strongest and most vile cheap liquor taste. I've used it (in combination with the meta-recipe below) to successfully drink such abominations as Smirnoff Vodka and McCormick Gin. With higher quality liquors that actually taste good, a quarter-ounce of lime juice can help the liquor blend more subtly with other ingredients in the drink -- compare a Cuba Libre with a generic Rum and Coke.

Because I'm a dirt-poor college student, I buy prepared lime juice in those cute little grenade-shaped plastic bottles. Bottled juice (even in glass, and especially in plastic) doesn't taste anywhere near as good as fresh lime juice, so those of you who want the best should squeeze it yourself. Professional bartenders prepare a big glass bottle of it before the night begins and mix from that. If you do this, please use glass and not some kind of plastic or metal that will flavor the juice. Also be sure to keep the bottle on ice, and shake it up before mixing from it.

If there's a gun to your head, lemon juice can be used instead of lime in most any drink recipe. Be warned that the drink will taste different, and probably won't be as good. Expect it to be more "sour" tasting, and the alcohol taste to be more prominent.

Here is my lime juice cocktail meta-recipe, called such because one can use most any ingredients and it will still taste good. It's the proportions that count. If you use everclear as the clear liquor, you will not be able to taste it very well, so be careful!

3 parts clear sweetened soft drink: 7up, tonic water, ginger ale, etc. Cranberry cocktail works too.
2 parts clear liquor: vodka, gin, tequila, everclear, etc.
1 part lime juice: squeeze it from a half lime, then drop it in to make the drink pleasing to the eye