In the Season 6 finale, when Monk finds the hitman who killed his wife, even though he has a gun with him, Monk just lunges at the guy and starts beating and kicking the crap out of him.
He also gets a couple of good moments when up against a shock jock. The episode deals with the insecurities Monk feels about his general lack of humour compared to the apparently hilarious DJ. He goes on the DJ's show and the DJ makes jokes about Trudy's death, prompting Monk to leap over the table and attack him. Then, at the end of the episode, when Monk's finally figured out how the DJ killed his wife and got him placed under arrest, he solemnly tells him "you're not laughing... now... are you?" Hudson says "No. I'm not" and Monk replies "Join the club".
Then there's his response when he manages to get his Arch-Enemy Dale 'The Whale' Biederbeck arrested for murder in their first encounter in the series; Dale, who is grotesquely overweight, lunges at Monk to try and throttle him, but can't quite reach:
Sharona Fleming: What's he doing?
Adrian Monk: [highly amused] I think he's trying to kill me.
[Monk leans in towards Dale, though he stays inches out of reach. Dale eventually gives up in frustration]
Adrian Monk: It wasn't much of a fight.
In the Season Four episode, "Mr. Monk and the Astronaut," Monk runs out onto a military airstrip and stands in front of an F-22 fighter to prevent the pilot from taking off to dispose of evidence.
And to top it all off, when it finally comes to a halt in front of him, he uses his sleeve to polish the nose cone.
Plus, he stands his ground with the laser sights of several rifles pointed at him, which had earlier caused him to completely flip out.
In the Season Two episode, "Mr Monk and the Paperboy" when reading a newspaper (he was trying to find out why someone would kill the paperboy over it) Monk solves a hit and run and a murder in France, before finding the actual reason the paper was stolen.
In the conclusion to "Mr. Monk is on the Run", Monk confronts Dale the Whale, who again proves to be the mastermind behind Monk's woes. Dale attempts to Hannibal Lecture Monk, yelling that even though he (Dale) is in jail, Monk will forever be a prisoner of his own hang-ups and defects. Monk responds by simply walking away, leaving Dale sputtering impotently in the background.
From the episode in which Monk gets his badge back is the confrontation with the murderer of a semi-corrupt cop. While Monk does fall for a Have You Told Anyone Else? moment, what happens afterward is all sorts of awesome - when said murderer tries to drop him from a scaffold by tilting and shaking it, Monk pulls himself up from the bottom, stabs said guy with his badge, and then throws away his gun before suspending him upside down from the scaffold, all while terrified by being a few stories from the ground.
Made even better by his one-liner when announcing his retirement from the force.
Officer: You're turning in your badge?
Monk: He has it.
In Mr. "Monk and the Captain's Wife", Monk jumps into a GARBAGE truck to solve a crime that personally affected Capt. Stottlemeyer.
This deserves elaboration. Monk and co have finally tracked down the man who sniped a truck driver, which directly lead to Stottlemeyer's wife being critically injured when she collided with the truck. However, they are unable to find the evidence needed to arrest the killer, namely his handgun that he had killed the victim over, and the victim's shoes. (the killer was barefoot during the shooting, and stole the victim's shoes to cover his tracks) Monk then realizes that today is garbage day, and runs after the garbage truck, jumps on and flings the bags out of it. Sure enough, both the killer's handgun and the victim's shoes are found in the bags.
The finale: Monk waits outside the culprit's house and makes him dig up evidence at gunpoint. While near-death from poison.
Monk: Your garage was open. I borrowed a shovel.
In "Mr. Monk and the Game Show", Monk realizes how a certain contestant has been cheating ( The host indicates the right answer by the corner he's holding the question card from) and makes it to the bonus round (to expose the murder) by defeating the champion with his own method.
In "Mr. Monk Stays in Bed", when Natalie is taken hostage by a criminal and brought to the dump in order to find a piece of evidence that could get him convicted, Monk manages to come in, tackle the guy, and then beats him down with trash long enough for the police to arrive. Oh yeah, and at the time Monk also happened to be sick and wearing nothing but his pajamas and bathrobe at the time.
Just to elaborate, Monk. Weaponizing garbage, his true nemesis. And succeeding.
Monk and Willie Nelson, on clarinet and acoustic guitar respectively, serenading Trudy's grave.
In the Tie-In Novel series, there's Mr. Monk and the Blue Flu, where Monk and Natalie are put in charge of the homicide division of the SFPD by the mayor. The mentally-impaired detectives he has all get some awesome moments, but especially Jack Wyatt, when he does a Shoot the Hostage ploy on a serial killer captured in a SWAT raid.
How about The Plan she pulls in "Happy Birthday, Mr. Monk"? She put one over on Monk.
Randy saves the day in "Mr. Monk Gets Married," when the suspect has married his much older mother. He finds the body of Padron's partner and arrives just in time (after Monk, Sharona, and assorted extras have been locked in a closet) to stop him from fleeing the scene and to heroically demand, "Where the hell is my mother, you son of a bitch?!"
Moments where Captain Stottlemeyer demonstrates Monk's power of perception: realizing a napkin from the suspect's coin store came from the crime scene where he claimed to have never been, figuring out Monk's new Poisonous Friend is using him because he knew a victim was beaten with a gun instead of shot, and solving a murder in Las Vegas just by looking at the inconsistency of the victim's earrings in photographs... while drunk.
Randy stopping criminals while dressed in Captain America PJs. While drunk. With a garbage pan lid for a shield. The only reason it works is that the criminals are still trying to figure out how to react when the proper, non-drunk cops show up.
In the span of a few seconds, Randy goes from being unarmed and sneaking up on a pair of killers to holding the gun in his hands and forcing them both to surrender. Moments like these we realize why he's still a cop...
Sharona giving a piece of her mind to a kid who threw a chalk duster at Adrian:
Sharona: Look, I know when a man's lying, okay? I was married for three and a half years.
Kyle: I didn't do it.
Sharona: I know that smirk. My husband had that same stupid smirk on his face when he got back from Bally's, where it turns out he spent the weekend with Betsy Bennett, his so-called "ex-girlfriend".
Kyle: Bally's, lady? What are you talking about?
Sharona: Is that chalk on your hand? Maybe I should call your parents.
Kyle: You don't have to. My dad's a gym teacher here, and he's gonna be pissed!
Sharona: I'm really scared.
Kyle: You should be.
Sharona then stamps on his foot.
Kyle: Ow! You're gonna get fired, lady!
Sharona: Yeah? I don't work here, chum.
In "Mr Monk and the End (Part 1)", Stottlemeyer needs some info from a fixer to catch Monk's killer. He tries yelling, he tries pleading for his friend's life, but the fixer taunts him by asking if Stottlemeyer is going to hit him with a phone book.
Fixer: People don't use phone books anymore! They use computers!
The writers get one at the end of the episode, when we find out Trudy's present for Monk, the one he never opened, contained a video message in case something happened to her. The same present they've mentioned throughout the entire series.
At the end of Mr. Monk and His Biggest Fan, Disher gets one. Throughout the episode, he had been wasting time playing a Jenga-like game, much to the annoyance of Stottlemeyer and the amusement of the others. When confronting the killer in a warehouse filled with large bundles of wood, Disher lifts out a long 4x4 piece of wood and shoves it back through the hole, hitting the killer on the other side and knocking him out. "Stupid game, huh?"
In Mr. Monk and the End, Stottlemeyer and Randy are racing to stop Monk from killing the judge. Their way is being blocked by a slow delivery truck which is reluctant to get out of the way, so Stottlemeyer pulls out his gun and fires into the air to make it move.
In Mr. Monk and the Dirty Cop, Natalie unflinchingly training a gun on someone.
In Mr. Monk Goes to Hawaii, we see Monk demonstrate that he can be protective of Natalie when someone tries to prey on her personal emotions.