Saddling up your faithful steed to ride off into the sunset is one of those things best left to John Wayne. Sometimes. Here are some of science fiction's best substitutes for our friend, the horse.
It seems that galaxies far, far away are the best places to go for horse alternatives. Whether they be the gualamas or Obi-Wan's varactyl, Boga, in Episodes I-III, or the more old-school tauntauns on Hoth or the Tusken Raiders' Banthas, there doesn't seem to be much of a shortage of rideable animals.
A Wrinkle in Time by Madeleine L'Engle
Although the immortal Mrs. Whatsit first appears to be an elderly woman at the beginning of the novel, she eventually transforms into a centaur-like creature with rainbows for wings, able to be ridden by the children.
Dune (series) by Frank Herbert
The desert-dwelling sandworms are very large, not particularly attractive, many-toothed, omnivorous, and somehow entirely capable of being ridden, although it really isn't a prospect for the faint-hearted.
"Rider at the Gate" and "Cloud's Rider" by C. J. Cherryh
The colonists of a hostile planet tame its indigenous horses, called nighthorses. They're intelligent, telepathic, and have a yen for bacon. (You'd think I was making that last bit up. You'd be wrong.)
Nightmare (Casper the Friendly Ghost)
Not a nighthorse this time, but an delightful ghost horse named Nightmare, friend and companion of Casper.
Comet (DC Comics)
Comet is the horse addition that rounds out all the superfluous super animals that had their heyday in the 1960's. Sort of Supergirl's pet, Comet was once a centaur in Ancient Greece, but due to an unfortunate potion, was turned wholly horse. Sucks to be him. (Although it seems he also gets to spend time as a human too, so there's a plus of sorts.)
Speaking of horses and ancient, nobody does a mythological horse better than Sleipnir, steed of Odin, king of the gods. This eight-legged creature was fathered by a stallion named Svaðilfari and birthed by Loki, the trickster god. And if you think about that too long, your brain hurts. (You can read a summary of the myth here.)
Dragonriders of Pern (series) by Anne and Todd McCaffrey
As the title suggests, the novels revolve around people who ride dragons on the planet of Pern. The riders have forged telepathic bonds with their dragons and use them to fight Thread, which is described as a deadly phenomenon that consumes all organic material in its path.
The Neverending Story by Michael Ende (and subsequent films)
Falkor the luckdragon, with his strangely serpentine, doglike appearance, flies the characters around, despite his lack of wings. (His unrelenting good luck is also a definite plus.)
My Father's Dragon by Ruth Stiles Gannett
To continue with the dragon theme, this young adult novel tells the fanciful tale of a boy (the narrator's father) journeying across an island to rescue a young dragon that had been captured by the island animals to ferry them back and forth across the river. (Find the full text of the novel here.)
Dinotopia by James Gurney (and TV series)
The sentient dinosaurs on the island work together with the people (who were shipwrecked there) to form a sort of utopian society, where all the inhabitants work together and the dinosaurs provide transportation for the people.