I generally pull the whole peel off, and then section it out. I don't think I've ever eaten a banana just by itself. It's usually accompanied with something else, so having it in sections makes it easier to squeeze stuff into it's flesh, or to place it evenly on toast. Sometimes I'll also put it in a blender with other things and spread it on toast or pita bread as a nice afternoon snack.
I don't take the peel totally off because I don't like touching the portion of food I'm gonna eat later I usually eat bananas after workout (i'm a runner) and my hands aren't always clean. Interesting question, lol XD
Depends if I eat it with bread... but I do open it from the opposite end of the stalk, apparently that's uncommon. But if you squish it it opens easily, instead of having to struggle (sometimes) with opening from the stalk.