From Nookipedia, the Animal Crossing wiki
The Giant Stag Beetle (オオクワガタ, Ōkuwagata); also known as Giant Beetle in Animal Crossing, Animal Crossing: Wild World and Animal Crossing: City Folk; or Giant Stag in Animal Crossing: New Leaf, is a rare insect found in every installment of the Animal Crossing series. It can be sold for 10,000 bells. It appears during the summer evenings, between the months of June and August, and between the times 11pm and 8am. It is extremely similar to the Stag Beetle, the only differences being that it is a bit darker and bigger.
Donation to the Museum
In Animal Crossing
"Your donation of such an obviously valuable insect is really quite generous. To me, however, it's just an overpriced cockroach. And that awful black luster...Horrendous!"
In Wild World
"If you took this to a shop, they'd be willing to pay you quite well for it, I'm sure. That said, all it looks like to me is a glorified, expensive cockroach! Perhaps that's just me..."
In City Folk
"The giant beetle boasts a massive horn, and yet it's said this bug is actually something of a milquetoast. Apparently this bug would prefer to stay inside where other creatures won't bother it. How precious. Even I could handle being near such a shy insect! I shan't be touching it, though..."
After donation, the Giant Beetle can be found on the top-most level of the insect section, three trees to the right of the lamp on the left-hand side, on the tree between the Walkingstick and Bagworm tree and the Saw Stag Beetle tree.
In New Leaf
Upon donation to the museum, the Giant Stag can be found on a tree in the back of the upper right room of the insect section. The exhibit has this to say about the Giant Stag:
Names in other languages