I believe MK's inspiration was a combination of Enter the Dragon, Big Trouble in Little China, Bloodsport, and ancient Asian mythology.
For example, the main story of MK1 was based on that of ETD, and Liu Kang was based on Bruce Lee's character from that film.
Raiden's design was based on the Three Storms from BTILC, but his character and name were taken from the thunder god of the same name (also known as "Raijin") from ancient Japanese mythology. Fujin's character, likewise, is based on the wind god of the same name from the same mythology. Both deities are depicted together in Japanese art, and likewise are associated with each other in MK, most notably in MK4.
Shang Tsung's role in MK1 was based on Mr. Han from ETD, but his design and character were based on David Lo Pan from BTILC.
Johnny Cage was based on Jean Claude Van Damme, and both his costume and his low blow move were taken from Bloodsport. Speaking of Van Damme, the MK1 project originated as an attempt by Midway to collaborate with him for a game, but that fell through when Van Damme signed to do a game with Sega (though that game was never released).
Boon and Tobias originally wanted to make a video game starring Jean-Claude Van Damme, but it didn't work out.
MK1 Shang Tsung is more or less your typical elderly martial arts master that you see in a lot of old martial arts flicks.
Goro was supposed inspired by the animated Kali statue in The Golden Voyage of Sinbad.
Kintaro is named after a character from Japanese folklore, noted for his strength. Originally, he was a anthropomorphic tiger, but Midway didn't have the means to create such a costume, so they made a modified model of Goro.