Java Edition:Dragon Fireball outside of The End
Dragon Fireballs can normally only be obtained in the End where the Ender Dragon is. However, from 15w33c to 15w44a, all fireballs shot by dispensers were dragon fireballs, allowing for them to be obtained in the Nether and Overworld.
Obtaining
Dispenser Glitch
From 15w33c to 15w44a (1.9 snapshots) all fireballs launched from a dispenser were dragon fireballs.[1] This is best paired with stationary projectiles to allow the dragon fireball to be stuck in place and therefore easily contained and put on display. The unloading method to obtain stationary dragon fireballs will only work in 15w33c.
Dragon in Invalid Dimension
The Ender Dragon can be obtained in the overworld or nether in several versions. Once it has been brought into the dimensions, it can launch the dragon fireball. The Ender Dragon's health must be brought below 75% health (150/200 health points) for it to exit its spinning and head towards 0, 0 in the world. Once it has been brought to that mode, it will fire dragon fireballs at the player.