Mammals:
* Aardvark
* Aardwolf
* Alpaca
* Antelope
* Armadillo
* Ass
* Aye-aye
Birds:
* Albatross
* Avocet
* Auk
* Anhinga
Reptiles:
* Alligator
* Anole
Fish:
* Angelfish
* Anemonefish
Insects:
* Ant
* Aphid
* Assassin bug
Other:
* Axolotl (amphibian)
* Acorn worm (worm)
* Anemone (coral animal)
This is just a small sampling, there are many other animals that start with the letter "A"!