NBA - The Splash Brothers
Those sumbitches changed the game by taking (and making) more 3's than 2's, and now a lot of teams including the Rockets revamped their rosters to try to keep up but fail over and over. It's hardly watchable now.
Good answer.
NBA - Magic Johnson
Magic (with Larry) rescued the NBA from the abyss. A 6'9'' point guard who could pass and handle the ball like him was... revolutionary. He had mad game, a singular style, great determination, charisma, a friendly personality, and a huge smile that could light up a room. A champion, and was the perfect fit for L.A.
NFL - This was the toughest one. Tom Landry
20 straight winning seasons, 5 Super Bowl appearances, and 2 Super Bowl wins. Much of the growth, maturity, and success of the NFL in the '80s and '90s came about as a result of teams following after trends that Landry began. Computers, situational substitutions, plentiful use of the shotgun formation, multiple offensive formations with creative play-calls, the flex defense, etc. Truly one of the great innovators -- and a big winner.
MLB - Pete Rose
Charlie Hustle was relentless. Broke Ty Cobb's all-time hit record. Had the 44 game hit streak that captivated the nation in 1978. Had a unique style and approach to the game, was a winner and champion. Captivated the nation again with his gambling scandal, prison term, and Hall of Fame ban. The most compelling MLB player of my lifetime.
NHL - Wayne Gretzky
I don't know hockey, but I know Gretzky. Is the all-time NHL points leader, and it isn't even close. Is almost 1,000 pts ahead of #2 (J. Jagr). Totally dominant.
Other Sports - Tiger Woods, Muhammad Ali
Tiger was well on his way to shattering Jack's majors record... before his dick got in the way. Whenever Tiger (in his prime) was competing, there was a buzz on the course. He had a level of skill that had not been seen before, he was a fierce competitor, and he had a flare for the dramatic shot. A golf madman.
Ali was Ali. The greatest. Legendary fights, tremendous heart and will. Incredible hand and foot speed for a heavyweight. His charisma and personality, combined with his great ability made him THE biggest sports draw of his era. A phenomenal smack runner -- ahead of his time.