This question gets asked a lot on the spirits forum, so I thought I'd give my two cents. Even though I'm more of a straight spirits drinker than a cocktail maven, I make my share of cocktails, and I especially like a cool cocktail as the mercury starts to rise and the heat sets in. There are lots of lists on-line lists of the basic home bar, and it gets asked a lot here on Chowhound, so I thought I'd take a crack at it. This is intended as the basic spirits and bitters you need to make standard mixed drinks. It's not intended to enable you to make every strange cocktail out there or to provide a selection of premium sipping spirits.
The Basic Bar
Bourbon or Rye (these are pretty much interchangeable in most drinks)
Liqueurs (It's always handy to have one or two of Amaretto, Kahlua, Bailey's, etc.)
Orange Liqueur (Grand Marnier, Cointreau, etc.)
Scotch (a standard blended - Famous Grouse or Johnnie Walker - will do for mixed drinks)
Tequila (100% agave)
Vodka (don't spend too much, it's just vodka)
Vermouth (a dry and a sweet...beware, unlike spirits, once opened these will not keep indefinitely)
This allows you to make a wide range of basic drinks: Martinis, Manhattans, daiquiris, Margaritas, Old Fashioneds, and such, but if you want to venture into more complicated territory, you'll need...
The Intermediate Bar (include all of the above plus)
Absinthe or Pastis
Bourbon AND Rye
Rum (a dark and a light)
After this it becomes more specific to the type of drinks you prefer. If you love Aviations, you're going to need creme de violette. Depending on what you like, you may need Benedictine, Drambuie or Chartreuse, but I wouldn't spend money on any of these unless they are ingredients in a particular cocktail you want to make. Maraschino Liqueur may be in that category as well, but it appears in enough recipes that I think it's worth having a bottle around. The good thing about these is that a little goes a long way. I have a bottle of Benedictine that's lasted me for years.
A few more basic bar commandments:
1. Use fresh juice whenever possible
2. Never buy simple syrup (it's sugar and water, for God's sake; it takes all of three minutes to make in a microwave)
3. If you want an easy way to experiment, there are lots of great bitters around these days; you can always throw some new fangled pear-artichoke bitters into your Manhattan and see what happens
4. There is no need to spend a lot on cocktail ware: a shaker, a strainer, a measuring cup and a muddler should be all you need
5. Don't wear one of those bartender vests. Just don't.
6. The people who spend a lot of time lecturing you about shaking versus stirring are the same ones who will lecture you about whether or not to put an "e" in the word "whiskey". That being said, the basic rule is shake any drink that includes egg, juice, milk or cream and stir drinks that are only spirits.
Thoughts? Changes? Corrections?