I have the Pampered Chef apple peeler/corer/slicer, which is absolutely amazing for making any apple dish. Works like a charm. I've never mastered the art of peeling apples (or peeling potatoes for that matter) and I don't plan to start now.
Just pull it off and the core is left behind. You can see the nice slices. It's like a continuous ring of apple slice, so I use a knife and quarter it (top to bottom) so the pieces are the right size. I also don't worry about the little bit of skin left on. Life's too short to be worrying about things like that.