"We've never lost an American in space and we're sure as hell not going to lose one on my watch! Failure is NOT an option!" Even thought we all knew how it ended, that was certainly Gene Kranz's CMoA. Kranz's autobiography, incidentally, is titled Failure is Not an Option. He also considers it his CMoA despite he never actually said it out loud, but that was the implicit spirit. His refusal to give up on the Odyssey crew can easily be considered another moment and awesome.
Kranz's unassuming but firm leadership. A role model; cool on so many levels, he's calm and collected, exactly what is required when time is at the essence, he makes critical and right decisions on his feet and never fails to be assertive but polite. When the occasion requires it he's stingy without being smug and proudly shoots down any defeatism. A perfect captain for any team, total badass.
The launch sequence. It was so realistic that Buzz Aldrin himself later asked where Ron Howard had found such great stock footage. A CMoA to the F/X folks!
If the launch didn't get you, the re-entry sure as hell will!
Just the movie in general. The director was so determined to get it right.
Examples include: Microgravity (they built interior LM/CSM sets within a KC-135 "Vomit Comet" jet and sent it on many parabolic runs to create true microgravity for the actors).
Incredible CG for the Lunar Module/Command-Service Module, especially at and after the explosion. See that cloud of debris (foil, gases and other junk) surrounding the LM/CSM from when they battle to stabilize the spacecraft to when they hit lunar orbit? Just as it should, based on physics; there's no air to shoo that away. The debris is gone as they make their way around the moon and back to Earth (a real-life/off-screen engine burn by the LM, just before the scene where they shut down the LM's computers and "put Newton in the driver's seat" made them accelerate away from their debris cloud).
The reconstruction of Mission Control was so right that one of the consultants, a NASA employee, kept forgetting it was only a set and looking for the elevator at the end of the day to leave for home, just like another "real" day back in Houston.
The scene with Mrs. Lovell (with daughter Susan) trying to tell her mother-in-law (who is recovering from a stroke) about the trouble her son is in, and the Cool Old Lady response. Hilarious,D'awwwwww-worthy, AND Awesome all in one.
(To Susan, who begins to cry):"You scared, honey? Well don't you worry. If they could get a washing machine to fly, my Jimmy could land it."
All the more cool when you realize that director Ron Howard had cast his own mother, Jean Speegle Howard, in the role of Lovell's mom. She got more lines than her husband, Rance ("Sheridan's Dad") Howard, who sat in a non-speaking role as the family priest near the end of the film. Ron completed his goal of casting his entire family with little brother Clint ("Tranya-loving Balok") Howard as NASA engineer Sy Liebergot, EECOM specialist.
Ken Mattingly, after being cut from the flight, is informed of the incident. First thing he does? Drive straight to Mission Control and work himself to the bone trying to work out the power up sequence, something that had not only been unpracticed, but was only conceived of for this mission.
In Real Life, it's even better: Mattingly was there at Mission Control the whole time.
Made better by the fact that, if he hadn't been on the ground, they probably wouldn't have made it.
The engineers get one where they have to devise a way to make a CO2 scrubber from junk on board the spacecraft
(Throws parts on the table) We need to find a way to make this fit into the hole designed for this, using nothing but that.
This is more dramatic, but actually less Awesome than how it was really done. The engineer who worked it out did so while driving in to Mission Control to solve the problem.
Given all that could have realistically gone wrong and with the slim chance of success that the return of Apollo 13 had, this is not a Crowning Moment of Awesome. It is THE Crowning Moment of Awesome.