NHL: Mario Lemieux. Being a left-winger, I eventually got biased and started loving Jaromir Jagr and Sergei Federov, but Super Mario was my first favorite player. I even had some skinny little biography book about him that I'd read over and over.
MLB: Ken Griffey, Jr. I was a lefty, so I loved seeing a lefty slugger. I also had SNES and N64, and his baseball games were the best.
NBA: Michael Jordan. Most sane people should say MJ, but as a Chicagoan, there's no other answer.
NFL: Barry Sanders. Never been a fan of the sport, but I've always been a huge fan of Barry Sanders, thanks mostly to my obsessive playing of NFL Quarterback Club 94.