In the Kanto games, and Johto games, there's a girl referred to as "Copycat" she will mimic the player. However, there is a tiny sidequest in which you need to get her Pokedoll back from the Pokemon Fan Club. In return, she will give you the TM Mimic, or teach you Mimic as a Move Tutor in their remakes. In the G/S/C and HG/SS she will give you a ticket to the magnet train.
She also has either a talking Doduo/Dodrio and Banette, as well as a few Pokedolls... in HG/SS, she also copies the players sprite exactly.
What did you think of the Copycat girl? Did you retrieve her Pokedoll?
I had no real opinion of her, because she was such a minor character in all the games she appeared in. I did get her missing doll in the Gen II games of course, but only because I needed the train pass from her.