The rule is the figure either has to closely resemble an animal or their name has to be the same (exact) name as an animal. Here's a few I have now:

Dogs:
Krypto
Lockjaw
Wolfsbane
Hepzipah

Monkeys:
Ultrahumanite
Monsieur Mallah (and the Brain)
Gorilla Grodd

Bats:
Man-Bat (HT and IC)
Vampire Batman
Baron Blood

Cats:
Cheetah (CJ and IC)
Catwoman (HT U and REV)
Catgirl
Black Cat
Hellcat
Tigra

Reptiles:
Killer Croc
Lizard
Princess Python
Sidewinder
Anaconda
Asp

Birds:
Vulture (FF and IC)
Songbird
Dove
Hawk (might be a stretch)
Hawkman
Hawkgirl (UL and IC)
Penguin
Black Canary
Raven (UL and IC)
Silver Swan

Insects and Arachnids:
Scorpion
6-armed Spider-Man
Queen Bee

Other Mammals:
Rhino


Any others? Also, what would Sasquatch and Wendigo fall under, anything?

Almost forgot, Hyena could go under dogs and Red Robin could go under birds.

Vixen can go under anything, though by name, she'd be a canine (vulpine to be precise - fox).

Arcane (spider)
Wasp (Some sort of insect???)
Ulik (saqatch)
Sasquatch (ulik)
Brood (bug)
Ambush (bug)
Hecate (ssnake)
Chameleon (bug)
Sabretooth (wolfman Jack)
Snowbird (bird??)
Wendigo
N'stirch
Mimic

what about owlman under birds

Kobra
Kobra Fanatics.

And the other bug-people:
Yellowjacket
Spider-Man (if Catwoman counts, he does)
Ant-Man

Deathbird
Hellcat
Nightcrawler
Black Panther
Black Cat
Spider woman
Toad
Beast..looks like a cat to me

Black Scorpion, Captain Mako (the shark-faced boy) & Lord Recluse from CoV (Brown Recluses being very nasty little spiders... never get bitten by one, it sucks)

Fury is a bat-winged thingy.

Um... everything else I can think of has kind of been said, already.

Blue Beetle?

(damn lack of an 'Edit' button)

Kobra
Kobra Fanatic
Batman
Batgirl
Robin
Black Canary
Queen Bee
Hive Trooper
Best
Archangel

and dont forgot arwyn and her dog. She could be the pet handler or something.