You shouldn't need to peel it if you've bought fresh stalks of tender asparagus, and properly trimmed the woody ends. I personally never do – probably because I never purchase overly tough asparagus in the first place. If you do happen to find yourself with a bunch of overly tough asparagus, though, there's no harm in using a vegetable peeler to peel any thick outer layer from the bottom inch or two of your asparagus spears after you’ve removed the woody ends.