Bulk, Skull, and the population of Angel Grove, and their re-enactment of the I Am Spartacus scene.
Followed shortly by another Crowning Moment of Awesome for Bulk when he rallies the citizens to enter the fray, fighting alongside the Rangers against quite frankly impossible odds. Then he throttles a Quantron with one hand.
The fact that the rangers morphed in full view of the public in the above scene. It can be taken as an awesome emergency action, or, more likely given the context, a sign of respect: On that day, everyone was a ranger.
The finale: holy hell, Earth's been enslaved by the bad guys and Bulk and Skull are the Big Damn Heroes! And the rest of the episode was just as awesome, even without knowing any of the context beforehand.
There's also the scene where Bulk very nearly wards off a monster by convincing it that a toaster is some kind of deadly weapon. Unfortunately Professor Phenomenous has to open his mouth and ruin it, but that took balls.
And Bulk, Skull, and Phenomenous blasting off in an experimental rocket to try to stop an asteroid from hitting the Earth. Man, they became awesome this season.
Both times Andros and Astronema fought one-on-one ("The Secret of the Locket" and "Countdown to Destruction") and the entirety of "The Rangers' Leap Of Faith."
Doubles as a Crowning Moment of Funny: Andros is walking down the hall, happy because The Psycho Rangers have been defeated—but look! There's Psycho Red, coming right at him! After a quick, heart-stopping fight, Psycho Red removes his helmet—it's Zhane! Who scared the living crap out of his best friend just for the hell of it! Go Zhane!
This only happened a few episodes after Zhane messed with the Psycho's heads as Psycho Silver, too.
The scene in "The Secret of the Locket" where Astronema zaps one of her own Mooks in order to prevent it from attacking two kids and their mother has always been a CMoA for me, due in large part to the audio. During the fights leading up to it, there's a lot of generic fighting music playing, but the minute Astronema kills her own Mook, there's absolutely no music at all playing. It reflected the shock and confusion that viewers (not to mention Andros, Ecliptor, and Astronema herself) were experiencing.
Following this, in "The Rangers' Leap of Faith", Astronema does the Reverse Mole turn to Gambit Pileup proportions, giving the Rangers a tip that leads them into a trap and then turning in a room full of mooks. She tells Darkonda to destroy the Rangers and once he readies to strike he is blasted and falls down, just like in the above scene. Darkonda is then finished off by some beams from a wounded Ecliptor, who fights his way through the mooks and supports his surrogate daughter in her Heel–Face Turn. Meanwhile, the Rangers form a circle around Astronema and Ecliptor and hold off a now angry mook army that wants to tear their Big Bad apart. Ecliptor does a Heroic Sacrifice, holding off a few dozen Quantrons and the like so to allow Karone enough time to escape. Poor Ecliptor, I always felt he was horribly mistreated by the Zordon Wave.
Carlos' return from his 10-Minute Retirement, where he anticipates the same position-switching trick the Monster of the Week fooled him with earlier and jumps off Adam's shoulders to nail it with his staff.
From the same episode, Adam morphing with his damaged original morpher. With a familiar yell of "MASTODON!", he becomes the black Mighty Morphin' ranger one more time, risking his life to do so.
Ecliptor's several-minutes-long fight with Darkonda in "Astronema Thinks Twice," including resisting the merging spell he'd been subjected to in an earlier episode through sheer force of will.
Alpha and D.E.C.A. (the Astro Megaship's computer) in "The Impenetrable Web," fighting off Ecliptor Home Alone style after he breaks into the Megaship.
One-Shot Character Waspicable deserves one for his Heel–Face Turn, taking a hell of a barrage of energy blasts from his former king and even running against them to get his own hits in.
Despite being a major Tear Jerker, the ultimate defeat of nearly all the evil forces and the ultimate sacrifice of Zordon during the climax of the "Countdown to Destruction" Grand Finale has to be, by far, the defining moment for Power Rangers as a whole.
I may be alone in this, but I personally felt that the first part of "From Out Of Nowhere" (yes, the first part of the very first episode) was spectacular. It sets the stage and tone for the entire season to a tee. In particular, the sequence that starts as soon as the Rangers' shuttle is docked with the Megaship outside of their control is simply astounding. They find themselves on board an empty ship, traversing the deserted corridors and even finding just-made food that has been abandoned; it's the kind of thing you'd expect from an Alien-esque blockbuster movie. It sounds simple in theory, but watching it, the tension is kept flawlessly high, ESPECIALLY if you'd just finished Turbo (and back in 1998, you'd probably have been waiting for two months to see what happened after "Chase into Sapce"). And this is Power Rangers. A so-called "children's show". Just...damn.
In "Wasp with a Heart," a good-hearted monster was shot and wounded by another monster, while shielding Cassie from the blast as she'd been overpowered and was helpless . When Cassie spots the injured monster, who she had grown to feel sorry for, in immense pain she turns down-right scary. At that moment, Cassie could have probably taken down Ecliptor and Astronema by herself unmorphed.
As a meta example, this season single-handedly SAVED Power Rangers. Ratings had been on the decline since Zeo, Turbo was loathed by audiences at the time, and Pokemon had officially taken the Saturday Morning crown. The production team, which had been divided over the show's direction during Turbo, banded together to produce a truly epic last hurrah under the assumption that In Space would be the final season. In Space's ratings were the highest since the MMPR days, and the series won over older viewers who left during Turbo and younger viewers just getting into the series. The critical acclaim and rating bump were enough to keep the show on the air. Without In Space, Power Rangers would likely be remembered as just another nostalgic fixture of the 90s rather than the kids action show mainstay it is today.
"Invasion of the Body Switcher" has a meta moment for Tracy Lynn Cruz, in her performance as Astronema pretending to be Ashley. Cruz manages to do a pretty top notch impersonation of Melody Perkins' speech patterns and body language.
Meanwhile, Ashley gets her own moment by tricking the monster into making her look like Astronema in order to trick Elgar into letting her go.