So I got this idea from the quiz site, Sporcle. In it, players had to click on an equine, feline, canine, feline. 
For example: zebra, tiger, wolf, persian until the options were used up.

I decided to bring it here, but altered for forum use.

I will name an equine. Player 2 will name a feline. 3 will name a canine and 4 will name a feline. And so on.

Acceptable: breeds, species, mythical (not one you made yourself).

SHIRE

Walkaloosa

ocelot

Poodle

Quarter Pony

^ this is a feline for Oak's equine post -- Sumatran Tiger

....so the person below me should post another feline...

Himalayan

Basset Hound!

cougar

Shetland Pony

african wildcat

alaskan malamute

rusty spotted cat

icelandic horse

Ragdoll Cat

pomeranian

european wildcat

Friesian

Khao manee 

Beagle

Mapogo lion