Around my house we see the Chinese egg case that looks like brown foam insulation about 2 inches long and often surrounding a plant stem. The mantid egg cases I left. During my wandering I had quickly made some decisions about good bugs, bad bugs and fun bugs to watch. Lady bugs are good bugs. The adults and young larvae have voracious appetites for those bad guys - aphids.
Tent caterpillars eat the leaves of fruit trees, birch and many other trees.
Mantids are in the fascinating category and not really as helpful in controlling pests as some garden catalogs proclaim. The young and adult mantids feed on just about any insect they can catch, including many beneficial insects, butterflies and each other. Mantids are nearly useless for pest control in home gardens because their diets are so diverse and they have poor survival rate. Most of the mantids that hatch from an egg case will die from starvation or cannibalism. Insects have all the elements of a good science fiction movie.