One of the things that makes cocktailian culture so endlessly fascinating (aside from the alcohol, of course) is the sheer variety of it all; aside from the infinite number of drinks and recipes out there, there are often several different ways to make a given drink (which brands of spirits do you use, and in what proportions?) and even good-natured debates on cocktail-making techniques.
Cases in point: the debate over at Jeffrey Morgenthaler's on straining vs. cracking, and Chico's interesting post below on shaking vs. stirring. As I noted in the comments, I usually follow the classic rule of shaking everything with juices or other harder-to-mix ingredients, while stirring drinks that are composed solely of spirits. And, as Jay points out, there's something in the silky texture of a stirred Martini that can't be matched by a shaken one...and the visual impact of a crystal-clear drink can't be beat either. But, it ultimately comes down to personal preference. (I once heard that Dr. Cocktail shakes everything, just because it's more fun that way, but I can't find any corroboration of that.)
But if you really want to get into it, check this pair of very detailed posts from DrinksCompanion: intensive discussions of both shaking and stirring. And yes, there are different schools of thought on how to do each of those methods: the posts take you through the various styles of shaking (including the Japanese "hard shake"), and the American, Japanese, and European styles of stirring. Informative... and I think I'll have to schedule a trip to Angel's Share soon to get another up-close look at the "hard shake" in action.