I've always assumed that the banana peel's only purpose was to provide cheap, slapstick laughs at the cost of some poor klutz, but it turns out that you can (and should!) eat the slippery bastards.
Photo by torbakhopper.
Not only are banana peels edible, but they're pretty good for you, and contain fibre, vitamins C and B-6, potassium, and magnesium. (The only people who should avoid them are those with latex allergies, as the peels contain some of the proteins that cause the reaction.) They can be blended into smoothies (along with the rest of the banana), fermented into vinegar, or cooked into tasty recipes like banana peel thoran or banana skins with blacked eyed peas. The riper the banana, the easier they will be to chew, but even the tougher ones can be softened with ten minutes of boiling (or frying, or baking).