Liu Kang (Ho Sung Pak in the first two games, Eddie Wong in the third)
Johnny Cage (Daniel Pesina in the first two games, Chris Alexander in Trilogy)
Kitana, Mileena and Jade (Katalin Zamiar in Mortal Kombat 2, Becky Gable in Ultimate)
Sonya Blade (Elizabeth Malecki in the first two games, Keri Hoskins in the third)
Shang Tsung (Ho Sung Pak in the first, Dr. Phillip Ahn in the second, John Turk in the third, Richard Divizio in Mythologies)
The Ninjas (Daniel Pesina in the first two games, John Turk in the third game, Ultimate and Trilogy)
Stopped Numbering Sequels: The first three sequels were numbered (II, 3 and 4), but every game afterward (when the series no longer had arcade releases) used subtitles instead (although the Deadly Alliance logo does have a huge "V").
"Additional" Fatalities. This may have played a part in future games giving characters multiple Fatalities.
There were also rumors you could play as Goro. (You could on the home consoles with the help of a Game Genie, but not in the arcade. He is playable in the Game Boy port if you enter a secret code after beating the game)
Probably the most famous example is Ermac. To elaborate, an early version of this game had a statistic in its DIP menu reading "Ermacs" (short for Error Macros) and sometimes it was said a glitch could turn Scorpion or Sub-Zero into a red-clad ninja fans named "Ermac".
Originally, Scorpion being a Palette Swap of Sub-Zero was meant to be an in-universe Take That; Scorpion donned a yellow version of Sub-Zero's uniform to mess with him. Said plot element seems to have been retconned though.
Sub-Zero's original name was going to be "Tundra".
Originally, a character named Kurtis Stryker was supposed to appear in Mortal Kombat. This character was replaced by Sonya Blade. The character that was supposed to be Stryker would appear in Mortal Kombat II as Jax. A different character under the Kurtis Stryker name would appear in Mortal Kombat 3.
Liu Kang was originally going to be called Minamoto Yo Shin Soo. He was a Japanese mythological character, but John Tobias stated that they could not deal with the name. The fact that it's a misspelling ("Yoshitsune" - and also not Chinese) also likely helped prompt the change.
There's an unused character design based on Cynthia Rothrock but that was never used, although Sonya's original design is said to owe a lot to Rothrock.
Rumor has it the game was originally intended to have Jean Claude Van Damme in it, and he was to be the hero of the story. Midway was unable to secure his services, however, so the story was retooled to center around Liu Kang, and Van Damme's character was retooled into Johnny Cage.
Network play was in test before DSL and cable internet were in wide availability. The test games used T1 Lines.
Raiden was originally thought to fight using a staff, but it was difficult to fit the weapon into the game's mechanics. The staff does appear in Mortal Kombat 4, which has a system designed with weapons in mind, but he doesn't actually fight with it until Deadly Alliance.
Speaking of Welker, he sneaks in a voice role as Shao Kahn himself at the end of the first film.
Fake Nationality: Japanese-born Cary Hiroyuki-Tagawa as Chinese-born sorcerer Shang Tsung. The more famous example is Trevor Goddard.
Real Life Writes the Plot: The fight scene between Reptile, Johnny Cage and Liu Kang was added after test audiences were dissatisfied with the other fights in the movie. Linden Ashby wouldn't have been on set.
Throw It In: Liu Kang was supposed to duplicate the acrobatic flips of Sub Zero's down the ramp during the fight, but Robin Shou couldn't pull it off successfully. After a few takes, instead of the acrobatics, he just ran down into the ramp yelling like a maniac. That's the shot that got used.