For some amazing photographs of the Bagworm check out Victor Engel's work: http://bugguide.net/node/view/135982/bgimage
The breeding habits of the bagworm are quite peculiar- the female is flightless and remains in the case for her entire adult life. The adult male must fly to her location and fertilize her eggs, which are laid in the bag where they remain all Winter. They hatch in the Spring and the young larvae disperse and make their first bags. Although this species is named for a mayfly (which the adult male slightly resembles), there is a greater resemblance to the caddisfly larvae which lives in water but also constructs a case out of sticks, sand or small pebbles. Now although caddisflies and bagworms are somewhat related, they are in separate groups and it seems unlikely that a common ancestor had the habit of constructing larval cases. So we may conclude that their shared habit of constructing cases for their larvae is probably an example of separate but convergent evolution.
So if you see bagworms on one of your valued plants you might just want to move them someplace else since they can do some serious damage. The simplest time to do this is in Winter when the bags contain hundreds of eggs and can easily be picked off the plants. But in any event let us marvel once again at the remarkable diversity of nature.
Englewood, FL & Galax, VA