In the same film: The ski sequence inspired by The Spy Who Loved Me (where he actually jumps from a cliff to an helicopter), Jackie fighting on stilts, and the final stunt: Jackie jumps a car onto a sailing boat!
Breaking his foot while filming Rumble in the Bronx, gluing his trainer uppers to the plaster cast and going right on with the stunts.
The whole film is a Crowning Film of Awesome (then again, most of his films are). He has a showdown with a hovercraft!
Special mention to his jumping through a shopping cart.
Demolishing the shanty town in Police Story, as later imitated by Bad Boys II
For that matter, the entire final third of the first Police Story, where Jackie goes absolutely insane on everyone that's wronged him over the course of the film. This includes him beating the crap out of the Big Bad, his doctor, and his lawyer, none of whom can fight. But they're such nasty bastards we don't care at all.
Rolling across a running circular saw in Mr Nice Guy. No CGI, no stunt double, remember?
Fighting with clogs in Who Am I?
And the climactic rooftop fight, just because so much of it takes place right on the edge. Really amazing watching three guys leaping around with so much gusto inches away from certain death with one wrong move.
The climax of Shanghai Knights doubles as a CMoA for both the villain: his effortless owning of Chan's character in a swordfight, and for Chan's character: he ends the fight by slashing the supports for the platform they're on, sending them both flying out the face of Big Ben!
Shanghai Knights also features the "Singing In The Rain" homage fight/chase scene. Of his North American films, this is probably Jackie Chan's most beautiful homage to the Golden Age films that inspired him.
When he descended from the highest floor of a mall by using a pole that had lights wrapped around it in Police Story 1. As always, no stuntman, no safety gears, one take. The electrical sparks caused by the light bulbs breaking as Jackie are all real. The outtakes of that film showed the aftermath.
Plus, some stagehand had plugged the lights into a regular outlet rather than the low-powered car battery he was supposed to. Jackie was quite surprised by the jolt.
At the end of Drunken Master, learning the style of the eight God, Miss Ho.
The climactic battle in Legend of Drunken Master. Almost fifteen minutes of Jackie beating and being beaten, whipped with a chain, falling into a burning pit, almost getting crushed, almost getting skewered by a fiery stake, relentless beatings at the hands of his enemies - until he realizes the fuel used to stoke the fires are 100% alcohol. It's better than spinach.
And, like always, Jackie does his own stunts, including FALLING ONTO A BED OF RED-HOT COALS! And he rolls on them for a bit before finally getting off of them.
A tag team effort from Rumble in the Bronx: Jackie hits a Mook a few times to get back at him for hitting his crippled kid sidekick. The man doesn't even blink, so the kid throws Jackie a football helmet. Even being whacked in the face with the helmet the guy still barely flinches. Then the kid throws Jackie an enormous pipe wrench, and at the sight of it the guy instantly goes down on his knees, whimpering.
City Hunter: Jackie Chan squares off against Gary Daniels while morphing into various Street Fighter characters, and if that scene isn't funny enough, the final showdown with Richard Norton is comedy gold.
Project A is particularly famous for the bicycle fight and Jackie's clocktower stunt inspired by Harold Lloyd.
Project A2: Jackie's final stunt remakes Buster Keaton's most famous stunt.
Police Story 3: Supercop: Jackie jumps from a building and onto a rope ladder attached to a helicopter already in the air. And remember, no CGI, no stunt doubles. Michelle Yeoh, in an equally impressive manoeuvre, jumps a motorbike onto a moving train.
As long as you've mentioned Ms. Yeoh, her best CMOA was arguably in the (mostly) Jackie-Chan-less Supercop sequel. While foiling a climatic bank robbery, Yeoh winds up fighting a huge brute of a man easily three or four times her size. After getting thrown around for several minutes and barely denting him, she eventually resorts to picking up two large bags of coins and literally running up one side of his body and down the other, over and over, while pummeling him with the bags, ending by landing gracefully back in front of him and assuming a ready stance, eyes locked with his, staring him down. Cue a looong pause … followed by the big lug finally keeling over. Yeoh holds her stance for one beat, then two … then lets herself drop in a heap with an exhausted gasp. The crowd goes wild.
Jackie Chan's fight scenes with kickboxing champion Benny 'the Jet' Urquidez surely count. Their battle in Wheels on Meals is considered one of the best fight scenes of all time. Years before the Matrix, no special effects, and it still looks amazing. Also, some Theme Music Power-Up for Jackie 2:00 into the video!
In real life, he's a Chinese musical pop star, as well as an action star who never has a stunt double, a martial artist, and a humanitarian. He also threatened to beat down any protesters who tried to stop him from running the Olympic torch to Beijing.
The Myth involves a scene in which he slaughters an enemy army single-handedly in close-range combat. He is wounded mortally in the process, but continues fighting regardless, despite the other side offering to allow him to surrender. When the opposing side finally resorts to shooting him with an arrow after their soldiers refuse to approach him, he props himself up by impaling himself on a spear on a ten-foot tall pile of bodies, and his body is still standing after the enemy general decapitates him.
A real life one: he describes in his autobiography how frustrating it was to make his first American film, The Big Brawl, because he was constantly restricted from making the fights and stunts as spectacular as he wanted. At one point, he proposed an elaborate stunt sequence in which his character would struggle to stay out of sight as his father's store was being held up, but the director told him to just walk right in. Chan proceeded to summon up pretty much all the English he knew at the time to declare "No one will pay money to see Jackie Chan walk!" And of course, he was absolutely right.