Sub-Zero is the only person to be a playable character in every Mortal Kombat fighting game. However, other characters have appeared in every Mortal Kombat fighting game.
Liu Kang appears Mortal Kombat: Deadly Alliance, but is killed at the beginning of the game, and is not playable. He is a playable character in every other fighting game.
Sonya Blade also appears in every Mortal Kombat fighting game, but only has cameo roles in Mortal Kombat II and Mortal Kombat: Deception.
Raiden has a special cameo appearance in Mortal Kombat 3 and the updated rerelease Ultimate Mortal Kombat 3, but is not playable. He is a playable character in every other fighting game.
Scorpion was not in Mortal Kombat 3, but he was added to Ultimate Mortal Kombat 3, and appears in every other game.
You may have noticed that I keep saying "fighting game". That is because there have been games in the Mortal Kombat series that are more action/adventure platformers than fighting games. These include Mortal Kombat Mythologies: Sub-Zero and Mortal Kombat: Special Forces, neither of which were well-received, and, despite being canon, are often not considered when one speaks of "Mortal Kombat games".