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Most adult insects have wings and most have two pairs. However some primitive insects do not, some have lost them as an evolutionary advantage, some have wings only as reproductive adults, and flies have only one pair with the hind pair adapted into 'haltares'. The forewing comes from mesothorax and hind wing from the metathorax.

Paleopterous - wings projecting out from the sides such as dragon flies and damselflies
Neopterous - ability to fold the wings back over their abdomen as in the majority of insects

Wings alone do not identify the insect. Some immature insects have no wings, and some orders of insects not listed here also have one or two pairs of membanous wings, but this is a guide.

Two pairs of wings. Front and hind wings of dissimilar structure:
Blattaria - Cockroaches: Tegmina (Tegmen/Tegmina - leathery wing)
Orthoptera - Grasshoppers, katydids, and crickets: Tegmina (Tegmen/Tegmina - leathery wing)
Hemiptera - Bugs: Hemelytron (Hemelytron - part leathery and part membanous)
Coleoptera - Beetles: Elyton (Elytron - hard sheath) meet in a straight line

Two pairs of wings. Front and hind wings of similar structure covered with scales:
Lepidoptera - Butterflies and Moths

Two pairs of wings. Front and hind wings of similar structure:
Odonata - Dragonflies and Damselflies: Front and hind wings long and similar in length and shape.
Hymenoptera - Bees and wasps: front wings longer and w/more veins than hind wings
Neuroptera - Lacewings and Antlions: highly networked wing

One pair of wings.
Diptera - Flies Haltares instead of hind wing. (Halteres - specialized organ to give stability in flight).
Paleopterous - wings projecting out from the sidesPaleopterous - wings projecting out from the sidesStigma - darkened cellMayfly  - Baetis sp.Leather tegmina folded over membranous hind wingsLeathery tegmina of Gray bird grasshopper -Shcistocera nitensMembanous hindwing of Gray bird grasshopper -Shcistocera nitensWing buds of immature Gray bird grasshopper -Shcistocera nitensHemelytron - part leathery and part membanous of Giant agave bug - Acanthocephala thomasiHemelytron - part leathery and part membanous of Small milkweed bug - Lygaeus kalmiiHemelytron - part leathery and part membanous of Say's stink bug -  Chlorochroa sayiElytron - hard sheath - Ground beetle - Calosoma sp.Lepidoptera wings covered with scales -California dogface - Zerene eurydiceMembanous wings covered with scalesScales covering butterfly and moth wingsWings held together - Marine blue -Leptotes marinaTypical wing position of skippersOpen wing position of duskywing skippers - Mournful duskywing - Erynnis tristisA 'tail' appendage onthe wings of a Gray hairstreak - Strymon melinusHighly networked membanous wing - Antlion - Family Myrmeleontidae