I will not pick just one character, but one from each gender.
Male- Scorpion
Scorpion has a pretty cool story arc when you consider not only his rivalry with Sub Zero, but also his role serving and struggling with and against Quan Chi in the Netherrealm. His moves in general look pretty cool, and can be pretty fun to play with. Hellfire and the harpoon both serve great purposes.
Honorable Mention- Raiden
He plays a huge part in the story, but I'm getting kind of sick of him.
Female-Kitana
Kitana is a great character regardless of being someone who has a weakness for long dark hair and blue stripper wear. She has a great story arc, and is one of the few characters that has a very strong role not only in Outworld, but in Edenia and Earthrealm as well. She does disappoint in one aspect though. She has the potential to be ultimately heroic in the storyline, but played only a slightly greater than insignificant part in the movies, and was almost completely lacking in the Deception Konquest. The lineage to Sindel and Edenian Royalty, rivalry with Mileena, adoption as Shao Kahn's ward, and romance with Liu Kang puts her right into the middle of the story, but she always seems to be marginalized. I guess MK developers neglect the feminist movement. She's the standout female character, but she still gets the shaft creatively.
That said she is quite possibly the most natural fighter to use in the game. Her fans are great spam, and her combos link very very well. The button combinations are smoother than most too.