The Rainicorn-Dog Wars refer to a war (or series of wars) between dogs and Rainicorns. In "Her Parents," Jake explains that it was a conflict over territory in the Crystal Dimension that lasted for thousands of years. It occurred recently enough for Bob Rainicorn to have fought in it.
Based on Jake's drawing of the war and the photo of Bob Rainicorn with the dog who saved his life, it seems that flying saucers were a part of it, and the dogs used laser guns. Jake's drawing also includes a mushroom cloud, which could imply nuclear weapons as well.
It is unknown which side, if any, was the ultimate victor of the war, though Bob and Ethel Rainicorn currently reside in the Crystal Dimension.
- In Bob's picture, the dog that saved his life is smiling and waving despite being in handcuffs.
- It seems to be a reference to the Korean War as it occurred in the wake of a major global conflict (the Mushroom War as opposed to World War II) and it pitted a Korean-speaking faction (the Rainicorns as opposed to the North Koreans) against a predominantly Anglophone one (the dogs as opposed to the United Nations Command).