She first appeared as an antagonist in the Final Fight cooperative fighting game from 1989, and has a very interesting origin.
Poison was originally designed as a newhalf by Capcom Japan. However, both she and Roxy were replaced by the male characters "Sid" and "Billy" for the Super Famicom/SNES home console versions of Final Fight released in 1991. Allegedly, this was done to appease concerns of players beating up female characters.
Rumours about her gender, coupled with her very sexualized design, gained Poison unusual fame. She also had cameos in several Street Fighter games and the VS. series, and made her Street Fighter debut in Ultra Street Fighter IV.
The (current, revised) official word from Capcom is that in Japan Poison is still considered a newhalf, while in America and the rest of the world she is a post-operated transgender woman.