The definitely used to spawn.
I thought they got rid of that with the breeding, but recently I've been finding there are more animals than I left so I don't know any more.
rebeljah-
No they don't despawn or respawn. Ever since the breeding update, the animals you get when you first load the map are what you get so, EAT MORE CHIKEN!
-faizedossss
If you cant find any animals near by just run out into the world and explore new chunks and when the are loaded for the first time new animals will spawn, I guess they're are still technically infinite so don't worry about running out!
EDIT: maybe you have something at this: http://www.minecraftwiki.net/wiki/Spawn#Animal_Spawning
I thought they got rid of that with the breeding, but recently I've been finding there are more animals than I left so I don't know any more.
A bit like villagers? I don't know, but that would make farming much more easier because you wouldn't need as much wheat...
Also, they don't mate unless you get them to personally. They just spawn in clumps of up to 4 at a time, so that's why they are grouped up.
No they don't despawn or respawn. Ever since the breeding update, the animals you get when you first load the map are what you get so, EAT MORE CHIKEN!
-faizedossss