Echoing Pyro's post...
I'm not sure about passerine type birds, but there is an "ino" mutation in psittacines (parrots).
I used to raise lots of different color mutations of cockatiels and Indian Ringnecked Parakeets. A wild-type Indian Ringneck is green with a red beak (the species is dimorphic with the males having a black neck ring and a rose neck ring... the female doesn't have either). A lutino mutation Indian Ringneck has a change in the coloration of the feathers and the bird is yellow (males have a white and rose neck ring) with red eyes. The lutino mutation is controlled by a sexed linked gene.
There is a different mutation in Indian Ringnecks that cause a blue colored bird with a black and white neck ring. The blue mutation is controlled by a recessive gene.
If the aviculturalist is careful, you can have both the lutino and blue mutations visible on the bird at the same time. The result is a solid white, red eyed parrot... an albino.
All of that to say is that you will see albinism in avian species as well as other species. Many commonly kept parrot species have a lutino / albino mutation.
The lutino / albino mutation can cause a "weak" bird. Cockatiels who have the lutino mutation, for example, tend to be smaller and have a large bald spot on the tops of their heads (under their crests) and overall don't seem to be as "fit" as a normal-type bird or one who has another mutation. These flaws can be minimized by careful selection of the parent birds.
Another example is albinism in humans is often paired with a significant reduction in one's ability to see. The person with albinism's eyes are more sensitive to light than a person who doesn't have albinism. I'm sure the same applies to any animal that is albino.
There are lots of albino fish commonly seen for sale: oscars, various African cichlids, tiger barbs, Corydoras catfish, etc...
There was a nest of leucistic American alligators found in a Louisiana swamp back in the 90's. The gators have blue eyes (not pink like an albino) and most of them are in various public aquariums around the US as I understand it.