Should asparagus be peeled before cooking? 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?
As a rule of thumb that would pretty much coincide with what JustRightMenus said: green asparagus is generally not peeled, but white asparagus should definitely be peeled. I think it's the same plant, just cultivated in a different way. (And interestingly, in Germany and the Netherlands, the green stuff is much less common, whereas in North America I've never seen the white ones.)