What is the significance of James Bond's famous phrase "shaken, not stirred"?

Is there really a difference in the taste of a shaken vodka martini, as opposed to a stirred one? And if there is, why?

Mark Langford, Stockport, Cheshire

The shaken-versus-stirred dispute has run for years in The Last Word. One of our books, How to Fossilise Your Hamster, drew on the first three answers below to explain the differences. However, we have since learned that other chemical reactions may be taking place - Ed