After going all-in with the "bow in the vague direction of France" portion of vermouth, I actually believe a good balance of gin and vermouth creates the perfect martini.

2 parts Cap Rock or Damrak gib
1 part Catoctin creek gin
1 part dry vermouth (Dolin)
2 dashes olive brine
1 dash Clear Creek Douglas Fir Eau-de-vie - optional

Shake with cracked ice, strain and pour into a cocktail glass.

Garnish with an olive or two on a skewer, or cocktail onions for a gibson. The Columbia Room serves their signature martini with a twist and a dash of orange bitters.

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.

Equal parts gin, campari and sweet vermouth, mix with ice in a lowball.

A juleped Old Fashioned or Manhattan

4 parts Mint Julep Makers Mark (or 3 parts bourbon mized with 1 part simple syrup muddled with mint)
2 parts Cognac
1 part sweet vermouth
1 part dry vermout
Dash Peychaud's bitters

Garnish with a cherry and a sprig of mint.

1.5 US fl oz Scotch whisky
0.85 US fl oz) Sweet vermouth
Dash Angostura bitters

Stirred over ice, strained into a chilled cocktail glass, garnished with a maraschino cherry or lemon twist, and served straight up, or mixed in rocks glass, filled with ice