Aska from the SNES version. There was even a petition online to make her a Canon Immigrant!
Casey Jones and April O'neil in Genesis version. The latter because she abandoned the Damsel in Distress role to be more of a fighter like in the comics.
Fan Wank: Is Hothead the same character as Chu Hsi from the Archie Teenage Mutant Ninja Turtles Adventures? Same background, as both are former human firemen possessed by a dragon spirit, and both are credited as being created by Ryan Brown, but even the TMNT Wiki treats them like separate entities, and Tournament Fighters is listed as being his debut. It doesn't help that his art on the cover is red (matching the "Hothead" action figure) while his sprite coloring is yellow (matching Chu Hsi).
Game-Breaker: There are a few moves that are a bit too good. Donatello's strong punch has instant recovery, deals tons of damage, stuns fast, fills up 40% of his special gauge when his life is on red, AND has very good range. The computer can counter this by magic reflexes, but against a human...
Leonardo's 'Millennium Wave' takes pretty much the whole screen, deals around 45% damage IF BLOCKED. But if it connects, it deals up to 90% more AND stuns the opponent.
Michaelangelo's Rising Thunder takes over 30% of life if it connects on the ground.
Raphael's biting grab in the NES version can be spammed to make getting through the game trivial.
Karai. Considered by many to be one of the most broken characters ever made in fighting game history. Her diving rapid punch special not only leads into a blockstun infinite, but it charges up her super meter incredibly fast. She also has a one-button infinite.
Unexpected Character: Some of the characters in the various rosters are relatively minor characters who managed to make it into the more well-known '87 cartoon (like Rat King and Chrome Dome,) and then there's a few characters (like War, Armaggon, and Ray Fillet) who only appeared in the Archie comics, plus Karai who at the time was exclusive to the Mirage comics, while Aska and Sisyphus are original characters. Basically if you were only a passing Turtles fan, most of the characters would be completely alien to you.
Vindicated by History: The SNES version. The NES version to a lesser extent (though the main strike against it is the game feeling a bit uninspired).