One of the most awesome moments from the Lethal Weapon series comes in Lethal Weapon 2 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him in the head through the diplomatic credentials he's holding up, uttering the infamous Bond One-Liner: "It's just been revoked!"
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."
In the first film, 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.
The way Riggs took out the guy who was sniping kids at the beginning of the film.
At the end of the first film, when Mr. Joshua makes a last-bid attempt at mayhem - MURTAUGH reacts first and fires before Riggs. Pretty awesome for an old man.
From part 3, the chase sequence that ends with Riggs gaining control of the armored truck he's in, fastening his seat belt (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.
From part 3, 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.