From Bulbapedia, the community-driven Pokémon encyclopedia.
A fake Pokémon is any non-official Pokémon. There are several ways in which one can be created and enter mainstream knowledge.
Assumptions of real Pokémon
Sometimes before the release of a new generation of Pokémon games, a silhouette of a new Pokémon will be released in Pokémon Wonderland, with the picture shown the following month. In that timeframe, sometimes fans will guess what the Pokémon will look like and draw up their assumptions. Others interpret these assumptions as the actual Pokémon.
In other instances, a false name or evolution of a Pokémon may be invented by a fan before any official release. Other fans, again, interpret these assumptions as fact.
Some assumed Pokémon include:
Fake items, with accompanying "methods of obtaining", were invented to evolve regular Pokémon into fake Pokémon. A "Mist Stone" was fabled to evolve every single Pokémon.
A common example of a well-known fake Pokémon is Mewthree. It appears commonly in fake cheats and fan fiction.
Rumors of Mewthree's existence within the Pokémon games have circulated since the first generation. Many fake methods were created, that were often impossible to perform or resulted in the player deleting their save file. These stories have led to a number of hack games focusing on this unofficial Pokémon. The most notable of these is Pokémon Chaos Black, in which Mewthree can evolve into another fake Pokémon, Mewthree X.
Mewthree was also one of the names given to the silhouette of Lucario early after its release on many internet forums because it appeared strikingly similar to Mewtwo.
Previously false assumptions
Sometimes fake Pokémon, though based on false assumptions at the time, coincidentally have real Pokémon appear in their place.
April Fools Pokémon
Often for April Fools pranks, Pokémon websites will create fake Pokémon and attempt to pass them off as recently revealed new Pokémon. These often include some of the commonly assumed fake Pokémon.
Some April Fools Pokémon include:
Other prank Pokémon
A fake sprite for the Sky Forme.
With the leak of Shaymin's Sky Forme in name, but without images to back the claim up, PurpleKecleon, a well-known Pokémon artist, created a fake version of this alternate form.
Needless to say, many in the fandom jumped to conclusions about its veracity, as the trademark on the terms "Land Forme" and "Sky Forme" had already been verified, while there was heavy evidence that Shaymin would be getting an alternate form. Thus, it became easily the most well-timed prank in the Pokémon fandom.
PurpleKecleon, however, announced the next day in her deviantART journal that she had created the fake Sky Forme Shaymin. The real one was leaked some time later due to artwork on drink cups from Pokémon Festa.
It is not unusual for fans to create their own fake Pokémon for pure amusement, often creating new elemental types and moves as well. These are usually openly displayed, usually on fanart websites or in hack games, and known about as being fake, though sometimes one may be assumed to be a real Pokémon by another fan, depending upon the skill of the artist and the gullibility of the fan.
In the anime
In The Ghost of Maiden's Peak, a Gastly, who had the ability to create illusions that were solid enough to attack people, created a crossbreed of a Blastoise and a Venusaur, calling it a "Venustoise".
In Malice in Wonderland, a Mismagius merged with a dream-made Rayquaza. It was looking like a shiny Rayquaza.
Several fansites have arose with a focus on fan-made Pokémon.