Java Edition:God Horse
In the April Fools' snapshot 3D Shareware, a horse with ridiculously high attributes could be summoned into one's world.
Obtaining
After typing the cheat code howdoyouturnthison in chat, the horse will be spawned near the player's location. This feature is exclusive to singleplayer, as cheat codes are not possible in multiplayer.
DemiGod Horses & Mules
Due to the mechanics of horse breeding averaging the stats of the 2 parents plus a randomly generated set, the offspring of God Horses will have significantly lesser, but still greatly overpowered stats. One may find these useful, such as the case of a DemiGod mule to carry more items quickly, or in general to reduce the speed and jump height to more user (and lag) friendly values.
Additional Information
The horse always spawned tamed, wearing diamond horse armor and a saddle and is always type 0. It has a high HP (Health Point) value of 200, however, only 60 HP is visible when mounted on the horse. For reference, the Ender Dragon has 200 HP. The speed and jump values of the horse are both 3.0, meaning it can run at approximately 126.5 blocks per second, and jump 34.34 blocks high. For example, the best possible natural horse attributes have a running speed of 14.23 blocks per second and a jump height of 5.5 blocks. This horse also lacks an owner tag, which is normally impossible for tamed horses.