From Nookipedia, the Animal Crossing wiki
The Koi (ニシキゴイ, Nishikigoi) is a rare fish found in rivers between 4 p.m. to 9 a.m. all year round. In Animal Crossing and Animal Crossing: Wild World, it can be sold for 2,000 Bells at Tom Nook's store. In Animal Crossing: City Folk it can be sold for 4,000 Bells at Tom Nook's store and in Animal Crossing: New Leaf at Re-Tail.
Donating to the Museum
In Animal Crossing
"Some fish bring a higher price at the market than koi, but koi are special in some indescribable way... For whatever the reason, catching a koi feels like... like catching a living fortune, somehow. Interesting, that. Well, aren't I incoherent! All rambling aside, rest easy knowing we will give this noble fish the utmost care."
In Wild World
"Hoo my! This addition should improve attendance at the museum most dramatically! I suspect that with the addition of this marvelous koi to the collection, folks from all around <<town name>> will be flocking to see it, wot wot!"
In City Folk
"...Great hoo! One of these should liven up the museum nicely, that's for certain! I say, I've heard a koi's worth is determined by how flashy its coloring is... Hoo now... How many Bells might this one be worth? ...Hoo, compose yourself, Blathers. This is for the museum!"
The Koi can be found in the middle-left tank, with other fresh water river fish.
In New Leaf
Once the Koi is donated, there is information on the board in front of the tank that houses it.
"Though typically pale in color, these aquarium fish also can be found with rather beautiful patterns. This is all thanks to very selective breeding of carp with genetic mutations, allowing for diversity. No two koi have the exact same pattern and are popularly known as "swimming jewels" as a result. They can be sold for a very high price, depending on their coloring and pattern. If properly cared for, they can live for over 100 years, making them a staple for outdoor garden ponds."
The Cyprinus carpio or 'Koi' as it is better known, is an ornamental fish of the common carp variety. They are found usually in private and public aquariums and they are bred mainly for decoration. Much as the goldfish, the Koi is also interbred from specially selected carp. Unlike the goldfish however, these are bred from common carp (Cyprinus carpio) and have a common body shape, but with different colors (the opposite of Goldfish). They are omnivores, feeding mainly on insects and algae. The name 'koi' comes from the Japanese, simply meaning 'carp.'
Names in other languages