The zebra group (there are several different species) are the only true wild equines remaining with the exception of the endangered Przewalski's horse.
A (quite pregnant) Grevy's Zebra mare. Source: Joachim Huber via Wikimedia Commons.
Zebras can be trained and ridden. Some circuses use them. There's a small market, especially in the US, for "zorses" - zebra/horse crosses, with the idea being that the resulting animal gets pretty zebra stripes and a horse temperament. However, because they are not a domestic species, they are harder to train and more aggressive than horses.
This has led to the myth that zebras were never domesticated because they are "too aggressive." The National Geographic article addresses this quite nicely.
Zebras were simply not the equine species that lived where people in Africa domesticated equines - their range was further south. Instead, they domesticated the ass - the ancestor of the modern domesticated donkey - as northern Africa dried out and cattle herders had to travel longer distances. However, zebras may have given us one thing - it's probable that natural interbreeding that occurs between zebras and wild asses where their ranges overlap gave humans the initial idea behind creating the mule.
An African wild ass. Source pats via Wikimedia Commons.
Asses were domesticated independently of horses but zebras, thanks to geography, escaped that fate.