Should asparagus be peeled before cooking?
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.)