According to some rumors, Gengar's double is Clefairy. Seeing that they are both the same size starts us off. Also, if you think about it, Clefairy is a Normal type Pokemon, while Gengar is a Ghost type. That may not seem weird at first, but when you think about it, it is.
You see, there are rumors that when someone sees their doppelgänger, it is a ghost of them, and they die when making eye/physical contact with them. Now, that is where their typing comes in. Gengar is a ghost type and the opposite to Clefairy. Also, since their STAB moves make them immune to each other, would you want to hit your shadow?
Now, they are even pretty close in appearance. They have the same distinctive:
it's said that Clefairy's back-wings became spikes on Gengar's back, and that Clefairy's curled hair is spiked on Gengar. Also, their tales are the same way, Clefairy's curled, while Gengar's was straight.
So in the end, these are the only Fan-made explanations that people have come up with. No one really knows except for the GameFreaks. But this makes you wonder...