Java Edition:God Horse
In the April Fools' version 3D Shareware V1.34, a special horse with ridiculous attributes was available. The horse always spawns tamed, wearing diamond horse armor and a saddle, and is always type 0. It has a ridiculously high HP value of 200, however only 60 HP is visible when riding. 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 reference, 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.
Obtaining
After typing the cheat code howdoyouturnthison, "VROOM!" appears in chat, and the horse will be spawned nearby the player's location. As the cheat codes are only available in singleplayer, this feature is not available 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.