When to Shake, When to Stir
This can be a hotly contested topic in cocktail culture. Both methods are used to both chill the drink and to melt ice into water to mix in with the other drink ingredients.It is instructive to know the basic effects either technique has on the ingredients.
Shaking a drink introduces small bubbles of air into the mixture as well as introducing some ice "flakes" that are broken off the ice cubes during the relatively more violent shaking process. This produces a somewhat cloudy drink and slightly effervescent mouth feel. Generally, you shake a drink when it is a contains fruit juice, cream, or eggs. These are ingredients that welcome the more energetic mixing technique of shaking. Examples drinks to be shaken are: Margarita, Cosmopolitan, Daiquiri, and the Whiskey Sour.
Stirring a drink is a more gentle process, and it leaves the drink clear with no ice chips floating in the drink. It is often said that shaking will "bruise" the spirit, although what "bruising" actually means is very vague. This technique is generally used for most classic cocktails such as the Manhattan, Martini, or Sazerac.
Regardless, now that you know what the effects are of each technique - go ahead and do what suits you at the moment. Want a Martini with small air bubbles suspended in the drink? Go ahead and shake it, it will still taste great.