Stable Keeper

Stable Keeper is a collection achievement earned for learning how to summon 10 ridable mounts on a single character. The mounts can be standard, swift, flying or swift flying. You need not use any of the mounts for these achievements.

Using an enchantment such as the one from Fresh Holly to change your mount will not count towards this achievement.

Strategies
A list of all available mounts is on the mounts page.

Somewhere in or around each of the racial cities or starting towns you'll find a merchant that sells mounts for that race. Each playable race has three or four normal land mounts available at level 20, and three swift land mounts available at level 40. To purchase mounts for other races of your faction, you will need to raise your reputation with that race's capital city to exalted.

Since patch 3.0.9, there are no race restrictions for purchasing mounts; tauren can ride troll raptors, and night elves can ride mechanostriders.

Three flying mounts are available to purchase in Shadowmoon Valley at level 60, and another 4 at level 70.

Each race has a mount they can purchase through the PvP rewards system. You are able to purchase mounts for other races of your faction, provided you are with the associated faction.

The highest-level tailors can build a flying mount.

Engineers can build a ground mount (Mekgineer's Chopper or Mechano-Hog) and two flying mounts (Flying Machine and Turbo-Charged Flying Machine).