They tend to be listed by type - largest moth, largest butterfly, largest beetle, etc, the weta bug from New Zealand seems to be the over all winner, but it's probably best for you to have a look through google and make up your own mind.
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Most people will place the answer in two categories, being the heaviest and the longest insects. The Giant Weta of New Zealand is the world's heaviest insect but the Phobaeticus chani Stick Insect is the world's longest bug, measuring 22 inches in length. It lives in the rainforests of Borneo. Photos of both can be found online by going to the two websites below.