The T-800's introductory scene, in which he goes into a pool hall and demands that a burly biker dude give him his clothes, his boots, and his motorcycle. When he disagrees, the T-800 wipes the floor with the patrons, which includes throwing the biker on top of a burning stove, and walks out of there dressed in the coolest black leather ensemble ever, made more badass when it's done to George Thorogood's "Bad to the Bone". The owner comes after him with a shotgun, and the Terminator calmly walks up to him, snatches the gun away, and grabs the guy's sunglasses. Forget the Tech Noir scene, this is the greatest Establishing Character Moment ever put to film.
The best part, he doesn't kill anyone.
Even better: this is before he was prohibited from killing anyone.
And if you've only watched the first film by this point (and missed the entirety of T2's ad campaign), you've probably assumed he was the villain again. Another dash of awesome on top of that.
The Galleria chase and the motorcycle chase right after. Those two scenes immediately establish that T2 is bigger, awesomer, and more explodey than anything that came before.
Sarah Connor's escape from Pescadero State Hospital, which involves beating an orderly senseless (he licked her face earlier, though, and beats her with a baton in a Deleted Scene), holding Dr. Silberman hostage with a syringe full of what is probably drain cleaner, and generally kicking ass (while unarmed, barefoot and wearing only sweat pants and a tank top). When the T-1000 goes after them in the elevator, she demonstrates that she is not the frightened damsel that she was in the previous film (as if it wasn't obvious already) by grabbing a pistol from the T-800's belt and shooting straight through the roof. She doesn't stop shooting until they lose the T-1000.
Especially this exchange:
Silberman: You broke my arm!
Sarah Connor: There are 215 bones in the human body. That's one.
Technically two (radius and ulna).
The T-1000 gets a few of his own in that scene, including becoming part of the floor in order to sneak up on a guard (whose form he then assumes after stabbing him in the eye), and walking through a door by shapeshifting around it.
After Sarah's assassination attempt on Dyson, it's John who takes control of the situation. Compared to the other examples here, it's very mundane, but it shows that even at the age of 10, he has the qualities of an excellent leader.
The Director's Cut also has him talking his mother down from destroying the T-800's chip. This is the Sarah Connor who was already plotting her own escape attempt and already made it partway out of the ward, and is very angry and very distrustful (and justifiably so) toward the T-800 due to her traumatic past with a machine that looks bang-on similar to the one currently helping her. And John doesn't dismiss her experiences or talk down to her, but merely asserts that they need the machine if they hope to have a chance of winning and that if he's meant to be the leader she wants him to be, she needs to listen to him. And she stands down.
Little Danny Dyson running over in front of Sarah, who's holding a pistol after shooting up the house with an automatic rifle, and flinging himself onto his dad's body, to prevent her killing him.
Don't hurt my daddy!
The Minigun Scene. The T-800 kicks a desk through a window, then opens up on the cops with a freaking minigun. Once the ammo for that runs out, he blows up their cars with a handheld grenade launcher. All with 0.0 casualties. An action movie that even makes NOT killing people awesome!
And right after that, he wades through the cops' fire in order to get close enough to shoot them in such a way where they'll live if they get medical attention. He really meant it when he promised not to kill anybody.
The T-1000 gets one immediately afterward when he drives a motorcycle into the building, up the stairs and out the window in order to hijack a helicopter.
The Car Chase that follows is the stuff legends are made of. They drive a police van out onto the highway, while the T-1000 follows in the helicopter, keeping it perfectly level about three feet off the pavement (including an incredible clearing of an overpass that looks to be evaded at the last possible second) . And shoots at them while doing it. The T-800 eventually gets the bright idea to let the helicopter crash into them, which gets rid of it as a threat but also disables their own vehicle. They end up commandeering a truck while the T-1000 follows in a liquid nitrogen tanker. John takes the wheel, and the T-800 climbs onto the hood of the tanker and shoots the T-1000 in the face repeatedly until they all crash into a steel factory.
Perhaps the coolest part of the T-1000 chasing them in the helicopter is a very easy to miss example of Mundane Utility. In a blink and you miss it cut, you can see the T-1000 has given himself four arms in order to pilot the chopper, fire the submachinegun, and reload at the same time.
The start of the chase is also heralded by a fairly simple exchange between the T-800 and Sarah, which, despite its brief length, does a great job of setting up the scene.
Once they're in the factory, the T-1000 has a little trouble moving in the liquid nitrogen before freezing entirely, and the T-800 tells him "Hasta la vista, baby," before shattering him into a million pieces. With a single bullet. He gets better, but that was still pretty damn awesome.
And when he starts to freeze solid, you can tell from the look on his face that the T-1000 is suddenly being faced with the reality that he is not invincible.
The T-800 finding an alternate power source and reactivating after being impaled and battered to the point it shut down, and the main theme starting up as he pulls the steel used to impale him out of his gut. It's like Kyle said in the first film, it will not stop.
That and his Big Damn Heroes moment as he rides the conveyor belt up to the platform Sarah and John are currently trapped on opposite the T-1000. Beaten to hell, a complete mess, with half an arm missing, he blasts the T-1000 in the gut with one last grenade. Cue one of the greatest Oh, Crap! faces on film.
Sarah gets yet another one near the very end, when the T-1000 assumes her form to try and trick John. She tells her son to get down, then blasts the Terminator from behind with a huge-ass shotgun, which she then pumps one-handed, and fires again, and again, and again, until the T-1000 is standing right over the edge. She runs out of ammo before she can land the killing blow, but that's where the T-800 comes in, riding a cog up and blasting the T-1000 with the last round of his grenade launcher, sending it into the steel below.
The scene is perhaps the best demonstration of Sarah having taken a level in badass. She goes from the standard Distressed Damsel in the first film to nearly being able to destroy the T-1000 on her own, without the T-800's help. And the reason they had her doing that at all was because Linda Hamilton had actually become strong enough in preparation for the film to rack a shotgun one-handed.
Remember that the reason Sarah was even doing her one-armed shotgun trick is because the T-1000 had previously stabbed her through the shoulder, twisting his finger in the wound for added effect, in order to get her to call out for John. She did not. Nor did she let the painful wound keep her from coming to her son's defense yet again. The glance the T-800 gave her after she attacked Miles Dyson? Likely that machine realizing that her single-minded determination to protect her child had transformed Sarah Connor into the closest thing to a Terminator a human can become.
Doubles as a real life moment of awesome too - the one-handed shotgun pump was not originally in the script. Linda Hamilton asked to do it to show off the conditioning and bodybuilding she'd done for the movie. She trained herself to be strong enough to rack a shotgun one-handed and, dammit, she was going to do just that!
Which, according to Word of God on the commentary, even Schwarzenegger couldn't do!
Another meta example with Hamilton: she learned how to do lock-picking for real for the Pescadero escape scene, and did picked the lock of the restraints on the bed and the door while the cameras were rolling. When the time came for the Britsh release, there was some struggling with the censorship board because they believed people would actually learn how to pick locks, just from seeing the scene.
Okay, this is from the Guns N' Roses music video. After the song we are shown a stinger with the band leaving the gig where they come across the T-800. As he walks past he identifies the band members by name, then when he identifies Axl Rose his Stat-O-Vision declares Waste of ammo, Arnie lowers the shotgun, and smirks. Yeeeeaaaahhhh.
During the Flash Forward in the prologue. We see a wave of terrifying killer machines rolling accross the battlefield, slaughtering humans left and right, but then we see another human soldier giving a crippled Terminator a coup-de-grace, followed by one of the flying Hunter-Killers getting knocked out of the sky by an Anti-Air missile. Even better, most of this was straight out of Kyle Reese's Flash Back from the first movie, except the last two bits happened after the flashback ended, making it a case of Once More, with Clarity!.
Every time the T-1000 sprints and runs like a demon and is just this close to grabbing its target. Implacable Man made even more awesome through sheer speed.
Even moreso is the fact that you never see the T-1000 looking winded or tired after a sprint. That's not special effects or camera work; that's the end result of Robert Patrick training with a sprinter to get himself to where he could sprint over fair distances without showing signs of distress afterwards.
Be honest: You want to be able to do Arnie's one handed shotgun flip, don't you?
The T-1000's incredibly haunting Dissonant Serenity is awesome in its own, terrifyingly understated sort of way.
Here's an example from a scene that was cut from the film but thankfully preserved in the novelization: A young Resistance soldier comes across another soldier that he identifies as a Terminator. Not from past experience or from nearby dogs barking, but because he was wearing the wrong color on his uniform (specifically, the color from last week). Without even hesitating, he fires a grenade launcher and blows it to bits before it even gets a chance to act. Even better? This was the same Terminator that Kyle Reese witnessed shooting up the Resistance base in the first movie.