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

Maine Coon

American Saddlebred

Bengal

Weimaraner ! 

American Longhair

Basuto

Savannah

Whippet

Russian Blue

Unicorn

Sabertooth Tiger

Borzoi

Scottish Fold

Lusitano

japanese bobtail

Bichon Frise

Norwegian Forest

Pinto ! 

Toyger

Goldendoodle