Although removing the entire banana is great when you are going to use the entire banana for something else (like in a smoothie), for good ol' banana eating, some may prefer to peel back the peel in separate strips as you go along, using the unpeeled part below as a handle.

http://chidiet.com/images3/banana1.jpg

When done properly, one's hands never have to even touch the fruit inside. Good for times on the go when washing your hands before eating is not an option.