I have it from two sources that asparagus should be peeled before being cooked in simmering water (Julia Child) or fried in butter (Heston Blumenthal). I tried Julia's method once and I've been discouraged from peeling them again ever since.
I probably overcooked on that attempt; they turned out a bit limp. But even so, don't asparagus look nicer with the skin on? And what's wrong with the skin anyway?
The asparagus spears I buy are quite thin with tender skin. Does the advice to peel only apply for thick asparagus spears?