- Mantidfly - Neuroptera
Mantidflies may resemble mantids or wasps, but belong with the lacewings in the order Neuroptera. - Pillbug - Isopoda
Woodlice, or pillbugs are related to crustaceans in the Isopoda and are not insects. - Twisted-wing parasites - Strepsiptera.
Twisted wing parasites like this one may be parasites of wasps or leafhoppers and belong to the order Strepsiptera. - Webspinner - Embioptera
Webspinners or foot spinners make silk with their feet and belong to the order Embioptera or Embiodea or Embiidina, depending on who you ask. - Beetle - Coleoptera
Beetles outnumber all other animal species on earth and they belong to the order Coleoptera. - Mantid - Mantodea
Mantids belong to the order Mantodea. - Fly - Diptera
Flies belong to the order Diptera. - Damselfly - Odonata
Damselflies and dragonflies belong to the order Odonata. - Roach - Blattodea
Roaches belong to the order Blattodea. - Earwig - Dermaptera
Earwigs belong to the order Dermaptera. - Scorpionfly - Mecoptera.
Scorpionflies, snow fleas, and hangflies belong to the order Mecoptera. - Centipede - Myriapoda
Centipedes are not insects, but rather belong to a related group in the Myriapoda (many legs). - Stick insect - Phasmatodea
Walkingsticks and leaf mimics belong to the order Phasmatodea. - Doglouse - Phthiraptera
While there is some disagreement on the exact methods for categorizing them, lice like this dog louse may be considered to belong to the order Phthiraptera (includes all lice) or separated into Mallophaga (just chewing lice) and Anoplura (just sucking lice). - Thrips - Thysanoptera.
Thrips for one, thrips for many (like sheep) belong to the order Thysanoptera.