They're not just delicious to us -- these plants in the carrot family are great hosts for butterfly caterpillars including these of the black swallowtail. This photo was taken by George Willingmyre who says:
Encourage Black Swallowtail Butterfly caterpillars to visit. Just plant some parsley in a pot or in the ground. We had planned to eat the parsley we had planted in the attached image, but don’t think we will after seeing all the caterpillars there. Here is a nice story about their life cycle http://www.pbase.com/rcm1840/lifecycleofblsw The site says these caterpillars like host plants in the carrot family such as dill, parsley, and fennel.