Moth

The Moth (ガ, Ga) is a nocturnal insect, that can be found on cloudy nights. Players seem to detest them even more than Cockroaches. Moths are usually found by bright lights. They can be found around outside lights from 7PM to 4AM in Population Growing, Wild World and City Folk. In New Leaf, however, they can be caught from 6PM to 4AM. They can be caught from May to September, and cannot be found in the rain.

In City Folk
"Many people hate moths, yet love butterflies, but the truth is that both belong to the order . Since both are covered in unspeakable veins and foul powder, I suggest they are equally distasteful."

The Moth can be found in the upper-left hand corner of the insect exhibit, flying around a lamp near the Bagworm.

In New Leaf
Upon being donated, the Moth can be found in the room of the bug exhibit with the light in, flying around the light. The exhibit has this to say about the Moth:

"Moths are related to butterflies, but they're most often active at night instead of day. They use their large antennae to sense, smell, and guide themselves in the dark. Interestingly, the number of moth species is estimated at 160,000, so "moth" is a fairly broad descriptor."