Why do chefs traditionally wear a high white hat?
Reaching back to my time in culinary school at Johnson &amp; Wales University in Providence, RI:

The style of hat originated in the Greek orthodox monastaries during the middle ages where chefs (often taking refuge with other educated members of society) would distinguish themselves from the monks by wearing a white hat (monks wearing black).  The early chef hats were slightly elevated but not as tall as they eventually became.

Marie Antoine Careme (commonly called "Chef of Kings and King of Chefs") is credited as the father of classical french cuisine for the development of mother sauces and standard garniture and classification of terminology used in kitchens.  He's also credited with much of the organization and division of labor in kitchens still used today.  To designate role and stature in the kitchen he had his cooks wear hats of various height.  His being the tallest designated him as the Head or Executive Chef. 

Traditionally it is said that the now traditional pleats indicate the number of ways that the chef wearing the hat can prepare an egg (of course this predates the disposable paper hats we now use).  100 pleats is considered to be the "ultimate" number to be desired.  However as a chef with 25 years experience in commercial kitchens, I'd be hard pressed to name 100 ways (without including eggs as an ingredient in recipes) to prepare an egg.