Here is a great site all about whistles http://www.whistlemuseum.com/ Thanks to Len McDowell and Avner Strauss for the tip.
Typically whistles involve air streams that flutter against each other. Take the typical whistle where the air rushes straight in and curls around. It has to break through an earlier part of of the air stream to get out the top. This creates an unstable situation, with the air streams fighting for dominance. They alternate thousands of times per second, creating high-pitched sound. If you could see the air bursts, you would actually see thousands of tiny vortices (like tornados) dancing around. The illustration in this link shows vortices being formed in a organ pipe.
http://www.e-scoutcraft.com/misc/whistle.html and here is a harder-to-make one out of wood. http://www.e-scoutcraft.com/wood_carving/whistle.html Thanks to Erik Bell for the links.
My friend David Williamson in London found a simpler way to make a whistel from a straw and cardboard. It's simiar to the ones made of sheet metal--but without the sheet metal, so even young kids can make them:
Here is a bit about whistle history. This page has an account of the invention of underwater whistles. Here is a site that deals with principles of sound. Shaku