In the first episode, a hungry T-Rex is staring Tommy (who, remember, at this point in time, has no Dino powers yet) in the face. Tommy's reaction? Do a spinning kick into its face before running for it. Let's say that again. He did a spinning kick into the face of a T-Rex.
Tommy Oliver: Green Ranger. White Ranger. Red Zeo Ranger. Red Turbo Ranger. Kicks Dinosaurs in the face. Is there any wonder why people consider him one of the greatest rangers?
Leading up to "Back In Black", when he morphs for the first time (in this series):
Tommy: There's two things you need to know about Dino Gems — one, you can't choose them; they choose you. Elsa: What's the other? Tommy(flicks wrist to reveal Dino Morpher): They go real well with Dino Morphers. (integrates Gem into his morpher) Elsa: Hmph. Aren't you a little old for this, Tommy? Tommy: I may be old, but I can still pull it off. (fires up morpher)DINO THUNDER, POWER UP!
The episode "Fighting Spirit," where Tommy is left comatose as an entire episode of CMOA for Tommy Oliver. Having beaten three previous incarnations of himself, he wakes up, heads for the battle, unlocks his Super Dino Mode and proceeds to utterly own the bad guy single-handedly.
Let's not forget that he beats his three previous incarnations WITHOUT morphing!
Not quite. Watch again, he doesn't actually beat any of them. He scores a few hits on the first two, impressing the Red Zeo and White Rangers enough to let him move on to the next challenge. And he actually loses the fight to the Green Rangerpretty handily, never once scoring even a single hit. When the Green Ranger hold him at daggerpoint, it's Tommy's willingness to go on anyway, knowing full well he's probably about to be die, that allows him to pass "the test". Crowning Moment of Awesome indeed, but for a whole 'nother reason.
Later on, Cassidy realizes her mistake and tells the audience during the news report the opposite of what her boss wants her to tell everyone, and puts her full belief in the Power Rangers, not caring about the risk of losing her job.
Conner, Ethan, Kira and Trent standing up and being willing to fight without their powers. In that one gesture, they accomplished a level of awesome that a season full of repeatedly shouting'Never give up!' couldn't match. And why do they do it? Because Tommy would.
After being unbrainwashed in "The Missing Bone", Kira rides into battle on the Pterozord. Unmorphed. Badass.
Episode 30, "Strange Relations". Trent vs. The White Ranger clone. An epic battle in which both are equally matched and Trent isn't using his Super Dino Mode while his clone does. The two decide to end their epic fight with a Single-Stroke Battle. The winner, Trent, who watches his evil counterpart go down with honor.
"I guess you wanted it more. Goodbye, White Ranger."
The first part of "Thunder Struck" was pretty much a Crowning Moment of Awesome for just about everyone.
Not least of which is Trent, who has just spent the past couple of episodes receiving flak from his teammates for not telling them that his father was the Big Bad of the season, single-handedly infiltrating Mesogog's lair and then proceeds to trick him to get the others onto the island. Bonus points for the Ironic Echo. "You should know by now you can't trust me." He then proceeds to grab the Dino Gems, run through a self-destructing building simultaneously dodging electric sparks and fighting Mooks to get his father and himself out safely. Made even better by Ethan's lines while waiting for the two of them to come out.
Ethan: "It's not like they're going to fall out of the sky and land in front of us." He then not-so-subtly checks the sky for Trent and Anton.
And of course, Trent and Anton pick that moment to come tumbling out of the sky. AWESOME.
Conner climbed onto a moving truck to fight Tyrannodrones while Hayley, the normal one of the team, powered up a laser to destroy Mesogog's fortress and then jumped off the moving truck just as the laser fired.
And Hayley ends up being the one to destroy Mesogog's fortress despite being the only Muggle on the mission.
The first appearance of the Thundersaurus Megazord. When facing an enormous airship, the new rangers grab the ship's cable, swings Tarzan-style to get above it, then promptly displays proper drilling technique to tear through its body and shred its engines. Entirely deserved dramatic explosions ensue.
When this is the first Megazord battle of a season, you know you've got something good.
Mesogog kicking Lothor's ass in the Ninja Storm crossover. Hell, the entire two-parter was awesome. From Lothor kidnapping Sensei and tricking the Wind Rangers into giving them evil power coins, to them kicking the Dino Rangers asses, to the two teams fighting each others UNMORPHED, Cam and the Thunder Rangers going into the Abyss of Evil, AND ALL 11 RANGERS IN THEIR BADASS EXPLOSION MORPH.
We then have Cam and Trent annihilating the Triptoids.
And pre-Lothor vs Mesogog, turns out Marah and Kapri — as in, the Plucky Comic Relief of Ninja Storm — betrayed their own uncle and rescued both Cam's father and the kidnapped Ninja Academy students. Now that's taking a level in bad-ass.
"Lost and Found in Translation". They actually went and made a nod to Super Sentai AND made a Take That! at both the Power Ranger and Sentai purists while making an absolutely hilarious yet fairly decent dub at the same time.
A giant-sized MOTW tries to stomp Conner in Triassic mode, and Conner stops the stomp one handed (his off hand, mind; he was still holding the Shield in the other) a la Cyborg Ninja against Metal Gear Rex, then goes one better and launches the thing about 30 feet feet into the air. There aren't many instances of Rangers displaying such levels of strength.
Goldenrod, Zeltrax's "son" being Ass-whooped by none other than Tommy, that too without a zord After Goldenrod Defeats the Megazord. He just uses the Brachio Staff's various powers and Solos him when he is at MEGAZORD SIZE. This is the legendary reminder for why we love Tommy Oliver.
Tommy Oliver gets 2 big awesome moments that have nothing to do with him being a Ranger and everything to do with who he is. One, he's the team mentor, which means that we get Papa Wolf Tommy Oliver, with every single skill he has at his disposal going towards protecting those kids. Two, Tommy manages to defeat his own insecurities about the past he regrets and is able to come to the realization that he matters not because he's [Ranger Color] Tommy Oliver but because he's Tommy Oliver.
There's more Awesome just by his personality. In the past, Tommy's explicitly said to have a bad memory. Which means he's worked his ass off to overcome his mental handicap and earn his degree. Now, he has a PHD. That's right. DOCTOR Tommy Oliver.