In a series this long, it's bound to happen from time to time. Since taking down any case can be one depending on the case, it's best to limit these to insane things such as in the 5th movie, Countdown to Heaven: The kids are stuck in a penthouse with a bomb about to go off. The only place they can escape to is the roof of a building about 60m away and 2m down. They have a car in the room with them, but it can't gain enough speed to make the jump. They use the explosion to boost the speed of the car by driving out the window right as the bomb goes off. Ayumi has to count down from 30 seconds exactly to time when the bomb will go off and when the car needs to start driving. Haibara decides she'll make a Heroic Sacrifice by counting down while sitting next to the bomb, but Genta jumps out and forces her into the car just in time to drive off. The explosion propels them far enough, but Haibara is falling out of the car because she wasn't buckled in. Mitsuhiko is able to grab her and hold on for the rest of the fall, but Haibara is out just far enough to be hit by some decorative pillars, so Conan takes the helmet he'd given Ayumi and super kicks it into the pillars, shattering them just enough for Haibara to graze by. They land the car in the other building's pool and are safe.
Don't forget earlier, when Ran and Conan are trying to escape from the same building, when another bomb set part of it on fire. The bridge they were going to use to get to the next building was blown up, and fire was closing in on both sides of the hallway they were in, cutting off all ways out. What do they do? Ran grabs a fire hose and ties it into a harness for herself and Conan. She then uses it to bungee jump out the window, knowing full well that all it has to do is break, and they both go splat on the ground. When the fire hose runs out, she ten pendulum-swings to the nearest window (which is on a floor not on fire), kicks it open, and climbs inside with Conan so they can escape.
Megure, almost always the Inspector Lestrade, gains a pretty good one in Episodes 218 and 219 by not only getting a pipe to the head to defend Sonoko from a psycho, but by also delivering a pretty epic "The Reason You Suck" Speech to the culprit. Despite being bleeding all over.
Similarly, Kogoro Mouri is pretty much the Butt Monkey and Defective Detective, but the end of the Hot Springs Episode from Season 1 is pure awesome. To sum it up: Both the victim and the killer are dear friends of his. Conan has found out first who is who, as always, but when he's about to knock Kogoro out as in every case... he hears Kogoro muttering to himself that he will catch the culprit even if it costs him his life. Conan is so moved that he can't bring himself to drug him, and instead he drops the hints Kogoro needs to resolve the mystery. And when that part is done? The killer launches a massive Motive Rant and attacks Kogoro. Said killer is a Genius Bruiser and pretty much 6 feet of pure muscle, while Kogoro is a scrawny Butt Monkey. Kogoro wins and easily pins the killer to the ground, which is followed with a short but badass Shut Up, Hannibal!. "No, I'm not the strongest in the judo team. It's just that you got weaker. You became a murderer."
Chapter 5: It's pretty awesome that Ran can stop a force hard enough to kill a small child with one arm. And also batter him afterwards.
Takagi, almost always the Butt Monkey, gets a big one when he's Alone with the Psycho, and then Satou (who's not alone, but with Conan and Co. but Takagi doesn't know that) calls him to his cellphone. The other notices and wants to force him to reply, putting the poor guy in quite the predicament because it'd make Satou come to his aid, and he doesn't want to put her in danger. What does he do? He takes a third optionand breaks his cellphone with his own hands, which not only screws with the killer's intentions but immediately tips off Satou, who calls the other police people so they can go help him. Takagi still gets shot and only his Pocket Protector saves him, but it was an excellent moment for him.
In Movie 9, Strategy Above the Depths, for the first time Kogoro manages to deduce and solve the case quicker and more correctly than Conan WITHOUT any hints whatsoever.
How did it happen? Mouri manages to point out that Akiyoshi but he has no proof and makes an excuse he needs to use the toilet. Conan manage to point out the culprit but realize his mistake and quickly rushes back to the ship using a jet ski before the captain is killed. Turns out that Mouri was right all along and manage to stop the assassination on time by dismantling her weapon when he actually went to the killer's room during Conan's deductions. Mouri figures out that the culprit might be a woman when he walk near her during the first murder.
The movies are especially prone to this due to their increased budget and role as summer blockbusters. This Troper is especially fond of Movie 8, Magician of the Silver Sky, where the plane and all its passengers are saved by the collective effort of Conan, Kid, Ran and Sonoko, of all people—including a holy shit moment when Hakodate Airport is SET ON FIRE by accident and Movie 15, Quarter of Silence, where Conan saves the day by snowboarding, causing an enormous avalanche to save a town from being washed away due to a broken dam.
How is Ran's moment from Movie 13, The Raven Chaser, not on here? Conan's all beaten up by Irish, and he tells Ran to get away when he saw her at the entrance of the observation deck. What did Ran do? She stayed, stood a couple of feet away from Irish, and dodged the bullet he fired at her. She then proceeds to launch some of her karate attacks at him. She may have lost the upper hand after a while, as Irish is much more experienced than she is, but damn, this girl is badass!
Chapter 830: Sera kicks Kaitou Kid in the head. Yes, that Smug SnakeGentleman ThiefKarma HoudiniKID, who always manages to get out unscathed from almost anything. Words cannot possibly describe the awesomeness (and hilarity) of that scene as well as the pleasure it will give you, so go look it up.
In one story, upon solving the case, Conan and Kogoro figure out that the three men who apparently owned the house they were investigating were actually thieves trying to loot treasure inside. When the thieves go to attack them, Conan and Kogoro manage to knock out all but one. That one tries to take Ran hostage. There's one panel of an Oh Crap reaction from the two men (including Kogoro actually telling the thief "Er, that isn't such a good idea...") before Ran uses her karate to knock the holy hell out of her attacker.
In the anime filler "The Victim Who Came Back" (Episode 303), Mitsuhiko actually manages to out-deduct Conan.
In Chapter 808, Satou goes Violently Protective Girlfriend and freaking jumps off a police helicopter to save Takagi from a cruel Death Trap in which he has been for two days. Then she shoots off the noose around his neck and tackles him so they can get away of the time bomb placed next to him.
Let's give Takagi his due credit, too. Despite being tied up, weakened, cold and completely defenseless, the guy manages to not lose the remains of his cool and keeps himself as poised and safe as his horrible situation, and drop some hints so someone can help him/the police can find him. Even more so: when he manages to untie his legs and try dropping the bomb away from him with his feet, he realizes that a group of kids is nearby and uses his legs to keep the bomb close so it won't explode near the children.
Makoto, the "Prince of Kick" who's undefeated in 400 tournaments from around the world, becomes Jirokichi Suzuki's world's strongest security system to protect the jewel from Kaitou Kid in Chapters 862-864. There's a list of awesome moments in these chapters:
To prove he's an asset to the police department, a video was taken showing a dozen bodyguards surrounding Makoto and aiming their guns (with BB bullets) at point blank range at him. Amazingly, he manages to catch ALL of the bullets fired at him and takes down the guards after they finish firing at him.
Not only did he manage to protect the jewel, he was even able to see through Kid's disguise when Kid was disguised as Sonoko by 'Sonoko's' index finger. However, Kid manages to escape with the jewel and ran away through the roof window while Makoto gives chase. How he manage to chase him? He kicks most of the pillars in the room and uses it as leverage and does a flying kick through the roof, shocking both Conan and Kid of his method. In the end, he manages to protect it due to Kid's bet on Sonoko.