Sub-Zero and Scorpion's introduction. As well as Raiden showing off how powerful he is by easily dispatching them.
Johnny Cage, Sonya and Liu Kang versus a gang of mooks, and what happened afterward:
Raiden: (after a slow, sarcastic clapping) Brilliant! Absolutely brilliant. So, why don't you show me what you plan to do about...(points behind the three of them) them?
(Sonya, Johnny and Liu see a small battalion of Mooks behind them, armed, ready, and advancing on them.)
Raiden: Uh-uh! (Mooks stop; lightning sparks on the tip of Raiden's finger) I don't think so. Heh, heh, heh. (Raiden lead the three out, as the Mooks clear a path for them.) I think you'll find that this is the way out.
Johnny Cage: (tosses his bo to another Mook) You guys are lucky he stopped us.
Sonya Blade gets her legs around Kano's head into a scissor lock:
Shang Tsung: Finish him!
Kano: No, Sonya, don't! Please! C'mon, gimme a break!
Johnny Cage vs. Scorpion. First, he kills Scorpion's organic spear by letting it embed itself into the tree behind him, gets sucked into an alternate Hell-like dimension, then battles him on the bridge before being sent down to the bone-filled ground. Then he uses the shield of one of the warriors that met their end below to protect himself when Scorpion tries doing his classic Fatality on him, just before hurling a spear his way, and then using the saw blade of the shield to slash him and take off the top of his skull-like head. Scorpion then fucking explodes.
Johnny Cage proving he's not just the Plucky Comic Relief by defeating the unstoppable Goro: immobilizing the Shokan with a Groin Attack long enough to escape, he forces Goro to chase after him. Goro finally ends up near a cliff, where Johnny ambushes him and knocks him to his doom. Brains 1, Brawn 0.
Cage: Those were $500 sunglasses, asshole!(Cue asskicking of Goro)
Say what you will about the quality of the film overall, but the Liu Kang vs Reptile fight near the end of the first film is pretty much exactly how movie fights should be done, especially the soundtrack. Despite being a rather random fight, there are reports of theater audiences erupting in cheers when Reptile appeared.
When Liu Kang and Shang Tsung finally go at it in the climax. While it's brief, seeing both Robin Shou and Cary-Hiroyuki Tagawa show off their martial arts chops is impressive. At one point in the fight (just before Shang Tsung summons undead warriors to fight Liu Kang), Robin Shou and Cary-Hiroyuki Tagawa agreed that Robin should actually hit Cary (with controlled force, but still actually make contact). The blow is in the film, and lends some extra weight to the moment Shang Tsung sees Liu Kang made him bleed.
Liu Kang's utter trouncing of Shang Tsung in the climax. "Flawless victory."
Right at the very end when the Emperor shows up... but the heroes aren't fazed for even one second.
Shao Kahn: You weak, pathetic fools! I've come for your souls!
Raiden: I don't think so! (Cue the heroes striking fighting poses as the credits roll and the theme song plays. The battle for Earth is on again!)
