Each playable race in WoW has its own mount: elephant-like elekks for the draenei, tigers for night elves, horses for humans, mechanical ostrich-like things called mechanostriders for the gnomes; massive rhino-like kodo for the tauren, raptors for trolls, living running birds called hawkstriders for blood elves, worgs for orcs, skeletal undead mounts for the undead Forsaken. It's always been the case that some mounts are available to others but not all, with constraints based on size. Lots of races can use tigers and horses, but only dwarves can join gnomes on mechanostriders.
Until today, that is.
In patch 3.0.8, the racial limits on mounts were removed. Now, it's still not super-easy to get another race's mount, because your character has to have a very high reputation with them. Not everyone wants to take the time to do the quests and gathering this requires. My friend who plays Tivara's questing partner Nyo, on the other hand, likes that sort of thing a lot, and uses it to break up the routine of leveling up. Her draenei paladin Akaa is indeed exalted with all five Alliance races, giving her the Ambassador title, and letting her be the first non-gnome I saw on a mechanostrider: