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

Standard Poodle

leopard

Brumby

lion

doberman

savannah cat

Morgan

Caracal

Mastiff

Snow leopard 

Clydesdale

Russian blue

beagle

Ocelot

pony of the americas

sumatran tiger

great dane

Barbary lion

norwegian fjord

cougar