The original mixture, according to The Fine Art of Mixing Drinks, is:

8 parts Cognac or Armagnac
2 parts lemon juice
1 part Cointreau or triple sec

Modern mixtures often have equal parts, I prefer roughly 3:1:1

Mix the ingredients in a shaker half full of ice. Strain and serve in a sugar-rimmed glass. Garnish with a strip of lemon rind

1 ounce rye whiskey
1 ounce Cognac
1 ounce sweet vermouth
1 teaspoon Bénédictine D.O.M.
2 dashes Peychaud's Bitters
2 dashes Angostura Bitters

From http://gumbopages.com/food/beverages/vieux-carre.html

Custom version:
4 parts rye bourbon
2 parts cognac
1 part sweet vermouth
1 part dry vermouth
dash of aromatic bitters
1 maraschino cherry

Instructions

Pour bitters, liquors over ice in mixing glass. Stir and strain into martini glass, garnish with a maraschino cherry.

Dive deep: http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2007/09/21/WI1ORSF9C.DTL

Variations:

A Dry Manhattan is made with dry vermouth instead of sweet vermouth and served with a twist.
A Brandy Manhattan is made with brandy rather than rye.
A Ruby Manhattan is made with port rather than vermouth.

Straight from the Jerry Thomas Bartener's Guide (http://en.wikipedia.org/wiki/Jerry_Thomas_(bartender) ) :

"In serving this drink you simply put a piece of ice in a tumbler, and hand to your customer, with the bottle of brandy. This is very safe for a steady drink, but thought a straight beverage, it is often used on a bender.

Combine in a shaker with ice:

The juice of 1/2 orange
The juice of 1/2 lime
The juice of a lemon

half oz of brandy
sweet syrup to taste

Add a nice fruit-forward red wine (jammy cabernet blends work well)

Shake to chill, serve in a margarita glass with plain soda or ginger ale, garnish with orange and lemon slices plus berries and mint sprigs