Kodo mounts are mostly Horde only mounts. They were originally added as a replacement for [Plainsrunning] (a tauren ability).
Factional mounts: Apprentice
You can purchase these mounts from Harb Clawhoof <Kodo Mounts>, in Bloodhoof Village in central Mulgore so long as your character has riding skill of 75 (obtainable at level 20). If you are playing as any race other than a tauren, you will also need to have Exalted reputation with Thunder Bluff.
Factional mounts: Journeyman
You can purchase these mounts from Harb Clawhoof <Kodo Mounts> as well, so long as your character has riding skill of 150 (obtainable at level 40). They are reputation restricted like the apprentice mounts.
See also: TCG Card.
Other Kodo mounts
These following kodos can be purchased from the Argent Tournament. You must have completed [Champion of Thunder Bluff] or be a tauren to gain access to this quartermaster.
Tauren paladins gain the ability to summon the Sunwalker Kodo (apprentice level mount) at level 20, and the Great Sunwalker Kodo (Journeyman level mount) at level 40.
The [Great Brewfest Kodo] is a drop from Coren Direbrew in Blackrock Depths during the annual Brewfest event. It is the only Kodo Mount available to the Alliance.
The [Black War Kodo] is available from Raider Bork <War Mount Quartermaster> in Orgrimmar for 15 Marks of Honor.
[Vicious War Kodo] can be purchased with a [Vicious Saddle] from Deathguard Netharian.