From Nookipedia, the Animal Crossing wiki
Mosquitoes (カ, Ka) are insects that fly around on warm summer nights, making a high-pitched buzzing noise. They bite the player when they reach them, causing the player to rub the insect bite. If the player is fishing, he or she will immediately stop fishing to rub it, pulling in the rod in the process and failing to catch the fish. Mosquitoes are tiny and difficult to spot aside from the whining noise they make when they fly. They will also chase the player a short distance, but are easy to outrun.
Donating to the museum
As with all bugs and fish in Animal Crossing series, the Mosquito can be donated to the Museum by talking to Blathers, the curator. Upon donation, he will tell the player a little about the donation. Below is what he says in each game:
In Animal Crossing
"I'm rather impressed that you managed both to capture and transport a mosquito here without squashing it. I might've squashed it just on general principles, wot! So, <player>, how's your mosquito knowledge? Were you, for example, aware that male mosquitos can't drink blood? No, they survive by drinking plant nectar. Evidently, the female is the vampiric one, and she only ingests blood for the protein she needs to lay eggs. I couldn't care a fig myself. All I know is the itching that occurs after one is bitten is quite disturbing. Not only that, but mosquitos are notorious carriers of all sorts of disease, you know! Dirty, filthy little buggers!"
In Wild World
Despite his objection with the insect, Blathers will still give the player a little info on it:
"I don't begrudge mosquitos the blood, for all creatures must survive, eh wot? But why, oh WHY must their little nibbles itch so much? They're maddening! Hoo... Then again, who am I to question the infinite web of nature, wot wot?"
When bitten by a Mosquito, the player will say "I got bit by a mosquito! So...very...ITCHY!"
In City Folk
"...Hoo, yes, are you aware that mosquitos serve as a vital source of information for the academic world? Indeed, many germs live inside of mosquitos and use them to travel across the entire globe. By understanding the living hosts to these germs, scientists may develop new treatments, eh wot?"
It can be found flying near the lone palm tree in the middle terrace of the insect exhibit. It bites the player when he or she stands still for too long.
In New Leaf
"Mosquitoes can easily be found flying around on warm summer nights looking for targets. Only the females feed on blood, and when they do so, they also inject saliva. The saliva is actually what causes the annoying itchy feeling, rather than the bite itself. Mosquitoes detect body heat, sweat, and carbon dioxide, so they are drawn to exercising humans."
When players have caught the Mosquito, they can find information about the insect in the bug menu. Below is the information regarding the Mosquito:
Names in other languages