Riggs dealing with the building jumper in the most Riggs-y fashion possible.
The shooting range scene where Riggs draws a smiley face on the paper target.
"Do you sleep with the thing?"
"I would if I slept."
The way that Riggs snapped the neck of Endo, who was about to electrocute him — and then proceeds to enter the boiler room and open up a can of whoop-ass.
Riggs throwing down the gauntlet to the dangerous Mr. Joshua with zero fear.
What do you say, jack? Would you like a shot at the title?
The way Riggs took out the guy who was sniping kids at the beginning of the film.
At the end of the film, when Mr. Joshua makes a last-bid attempt at mayhem - MURTAUGH reacts first and fires before Riggs. Pretty awesome for an old man.
Murtaugh taking out McAllister when the latter tries to make a break for it.
Murtaugh: (doing his signature neck crack) No way you live. No way.
Lethal Weapon 2
One of the most awesome moments in the series comes after Riggs is thrown off the docks to drown in a straight jacket after he finds out that Vorstedt was responsible for his wife's death (and soon finds out he is responsible for Rika's). He dislocated his shoulder to escape and then killed the two "mooks" guarding the dock by breaking one's neck and slamming a car door into the other one's face until he died. Only after that, did he pop his shoulder back in.
The other moment is the death of Rudd, who has been using his diplomatic immunity to escape justice throughout the entire film. At the end of the film Rudd shoots Riggs and tries to use diplomatic immunity to escape yet again, to which Murtaugh just takes aim and shoots him in the head through the diplomatic credentials he's holding up, uttering the infamous Bond One-Liner: "It's just been revoked!"
Murtaugh taking out two bad guys with a nail gun. "Nailed 'em both".
Riggs pulling down the bad guys' house with his car.
The final fight between Riggs and Vorstedt
To elaborate Vorstedt surprises Riggs by throwing a knife at his leg then following up with a series of kicks. Even a knife stuck in his leg, Riggs still overpowers Vorstedt. Then, when Vorstedt tries to dig the knife further into his leg, Riggs grabs onto his arm, uses it to pull the knife out and then stab Vorstedt with it before finishing him off by dropping a shipping container on him.
Lethal Weapon 3
The demolition of the ICSI Building at the beginning of the movie. The explosion is considered one of the most memorable scenes in the entire series.
The chase sequence that ends with Riggs gaining control of the armored truck he's in, fastening his seatbelt (which you never see in an action film), and then coming to a screeching halt, sending the bad guy flying through the windshield.
Riggs: You have the right to remain unconscious. Anything you say... ain't gonna be much.
Lorna Cole joining up with Riggs (and later Murtaugh, after he bounces out of his depression). She's just as skilled in hand-to-hand combat as Riggs is and more.
The insane part? Donner actually had to tell him to slow down because he was moving faster than the camera could register.
It's been said that Jet Li's kicks fill a fraction of the frames that a camera uses in a second of film. Something about 7 out of 21?
The last use of "One, two, three, go!" at the end of the movie. Doubles as a Heartwarming Moment.
The final fight between Riggs and Wah Sing Ku. The best part is that between Jet and Riggs it started out as one-sided until Jet dislocated his shoulder.
Before that, Riggs and Murtaugh catching his legs and throwing him down when he tried to do a midair kick. It was from that point they slowly started to regain the upper hand.
Riggs and Murtaugh crashing the deal between the Corrupt General and the Triads, all by acting irreverent and giving a piece of scrap paper to the General. Cue the enraged General gunning the Triads down while the duo ran away and let them kill each other. Also doubles as Funny.