Family Equidae has but one surviving genus, and that is genus Equus.

There are eight currently existing species of Equus, all of which can interbreed and produce non-viable offspring, but do not normally do so in the wild.

Equus przewalski: Przewalski's horse and Riwoche horse.

Equus caballus: domestic horse and pony.

Equus asinus: North African wild ass and the domestic ass (AKA ass, burro, or donkey)

Equus hemionus: AKA "half ass" (sorry, but there it is). Asiatic wild ass, onager, and kiang.

Equus grevyi: Grevy's zebra or Imperial zebra. (15 thin stripes on flank).

Equus burchelli: Plains zebra or Common zebra. (5-6 thick stripes on flank).

Equus zebra: Mountain zebra. (12 thin stripes on flank).

Equus quagga: Quagga (Now extinct, as of 1883.)

It is interestering to note that while these animals can interbreed to produce living offspring, they all have different numbers of chromosome pairs (33, 32, 31, 27, 23, 22, 16, and ??, respectively).