The CIA heist in the first film, showing that an intense scene in a summer blockbuster can be done without explosions and body count, but with an emphasis on silence.
Tom Cruise's ongoing pattern of unbelievable commitment to the projects, from risking his life to do various stunts to meeting fans at four different premieres for Mission Impossible III within four hours, having personally piloted his helicopter between them, to conducting the freaking orchestra for the Mission Impossible theme.
Just a taste of going the extra mile for the stunts: That sequence in the second film where the blade of Ambrose's knife comes within a quarter-inch of Ethan's eyeball and then Ethan and Ambrose struggle for control of it? That is a real knife being held a quarter-inch from Cruise's own eyeball per his request for the take.
That's Cruise scaling, running, and flying over the surface of the Burj Khalifa in Dubai without a stunt double in Ghost Protocol. The Burj Khalifa, only the tallest building in the world, no biggie.
The effects department gets a big one for the Owen Davian mask scene in Mission Impossible III. Pure movie magic.
The climax at the end of the first M:I definitely deserves a mention, but it wouldn't be complete without the music. Until this point, the music has been this cacophony of musical instruments. But when Kreiger nearly loses control of the helicopter before you think he slices Ethan's head off, the music does the M:I equivalent of a "CHARGE!!!" and then blows out the M:I Theme crystal clear in a different key in a musical equivalent of "And the fight is on!". It's so awesome it makes this troper smile and get goosebumps.
Not only that, the fight itself is an awesome case of better than it sounds: "Surfing on a train with a helicopter inside a tunnel, and the bad guy is defeated by gum"
The sequence is so Rule of Cool that even Roger Ebert admits in his review that even though there's no plausible way a chopper could fit inside the Chunnel and have room to maneuver, it looks so damn awesome that you simply let it go.
Let's not forget the scene immediately preceding the fight atop the train. Ethan ruins Phelps' entire plan just with a pair of glasses.
"Good morning, Mr. Phelps."
The Vatican Heist in the third movie. The team infiltrates the Vatican, slips past security, gains access to underground tunnels under the building, photographs the bad guy, creates a mask that is a perfect replica of his face, captures him and lets a disguised Ethan take his place after which they fake his death by blowing up a car, so that his entire entourage thinks he's dead. Wow.
In "Ghost Protocol", Ethan climbs the highest building in the world, courtesy of sticky techno gloves, only for the devices to crap out on him when he makes it to the server room. How does he get back down? He pulls a John McClane by wrapping a cable around his waist and jumping out the window, proceeding to RUN STRAIGHT DOWN THE SIDE OF THE BUILDING, accompanied by Giacchino's awesome rendition of the M:I theme. It's a helluva Theme Music Power-Up.
Perhaps the best evidence of Hunt's unbelievable ball size would be the final fight sequence of Ghost Protocol, which peaks with the bad guy jumping six stories to his death simply to deny Ethan the MacGuffin, and Ethan driving a car off a ledge after him, hoping the air bag will blunt the damage enough for him to remain able to crawl upon landing. It works... After crashing, he is able to drag himself over to the MacGuffin with his arms.
In Ghost Protocol, Benji proving that he's more than just the computer guy or the plucky comic relief when he kills The Dragon who is trying to kill Brandt-with a look that is All Business.
Jane's entire fight with Sabine, starting with kicking off herheels to run after her, all the up to kicking her out of the Burj.
Phillip Seymour Hoffman deserves a medal for his performance as Owen Davian in the third movie. He goes from quietly sadistic to terrifying rage AND BACK in a matter of seconds.