A question that comes up often is: when do I shake a cocktail and when do I stir? The basic rule of thumb is this:
You shake any cocktail that contains juice, cream, eggs or other cloudy ingredients.
You stir a cocktail when the ingredients are all spirits.
I think this video from Imbibe (featuring Jeffrey Morgenthaler) demonstrates the difference well.
Sometimes I break the rules and shake my Manhattans or Martinis if I want little ice shards floating in my drink.