General:
* Pups: A common term for baby mammals, especially canines.
* Kits: A common term for baby rabbits and some other small mammals.
* Young: A general term for offspring of any animal.
Specific:
* Calf: Baby cattle
* Colt: Male baby horse
* Filly: Female baby horse
* Foal: Baby horse (both male and female)
* Lamb: Baby sheep
* Kid: Baby goat
* Piglet: Baby pig
* Cub: Baby bear, lion, tiger, etc.
* Joey: Baby kangaroo
* Fawn: Baby deer
* Kitten: Baby cat
* Puppy: Baby dog
* Leveret: Baby hare
* Cygnet: Baby swan
* Whale calf: Baby whale
This list isn't exhaustive, but it gives you a general idea of the terms used for baby mammals.