Female Pikachu with a heart-shaped dent in its tail
The short and simple answer is – NO! Pikachu never had a black tail in any of its various incarnations (except Cosplay Pikachu) over the years. Pikachu’s yellow tail does have a patch of brown fur at its base, but there is no hint of any black patch or black fur anywhere on its tail.
Even gender-based differences cannot account for people remembering a black tip on Pikachu's tail, as the Female Pikachu differs only slightly, its tail ending in a heart-like shape.
The only exception to this is the Cosplay Pikachu, a Generation VI video game character that appeared in Omega Ruby and Alpha Sapphire games. Cosplay Pikachu is a female and has a black heart-shaped patch at the base of its tail.
Pokemon XY episode 41 titled Lights! Camera! Pika! also has five Pikachu wearing said outfits, notes Bulbapedia. But this cannot be the source of the claims by some people regarding a black-tailed Pikachu, seeing that this conversation predates the games by years.