The end of the first episode: "Gummis... ATTACK!" Through a combination of speed, wit, magic, and Deadly Dodging, Cavin and all six Bears get past Igthorn's ogres and wreck the catapult he'd been using to attack Dunwyn. It's the first time they're seen in battle and makes it clear that the cute, brightly colored, little creatures are much stronger than they look. The perfect introduction!
Gruffi staying behind in "A Gummi In A Gilded Cage" so he could push the glider off the mountain and get everyone else to safety.
Zummi scaring away Igthorn and the ogres with his impersonation the Oracle in the episode of the same name, complete with an impressive blast of fire for the big finale.
The escape from Drekmore in "A Gummi By Any Other Name": Calla uses the Transformation Trinket to change herself into Igthorn, but it doesn't change your voice, and the only related spell Zummi knows makes voices much higher. Sunni gets the idea for him to cast the spell on the real Igthorn, making it impossible to tell which one is the imposter and confusing the ogres long enough for them to escape.
An ogre captures Grammi under a basket in "The Secret of the Juice." When he lifts it up, she's gone. While he's examining it, she falls out of the basket, drop-kicks him in the head, and sprints away.
Grammi proves herself to be a supreme Cool Old Lady all through that episode, remaining indominable and fighting back against Igthorn at every step despite her seemingly hopeless situation. Even when she is falling towards her death with no escape in sight, she does so not while screaming and flailing like you'd expect, but with a sort of unhappy "well, I guess this is it, then" grimace on her face, calmly Facing Death With Dignity.
Cubbi figuring out how to save the Gummiberries from the bird in "The Fence Sitter," prompting everyone else to realize they were wrong for telling him "Not Now, Kiddo!" for the entire episode.
Both Cubbi and Grammi share the awesomeness of "Gummi In A Strange Land" as they hunt down the slumber sprite that put Gruffi under its sleep spell. At first, Grammi finds that her slow-and-steady, carefully-think-every-step-through approach isn't much good when you only have a split second to make a move, so for most of the episode, Cubbi's actually the one who takes charge, running through a field of exploding plants, figuring out how to track the sprite, and scaring off a herd of sabre-toothed rabbits. When they actually find the sprite, however, Grammi's the one who convinces him to remove the spell by deducing that he's in trouble (because no sprite would willingly live in a place like Drekmore with no flowers that produce the honey they eat) and offering to help. She then charges into a quartet of ogres to save Gruffi, making for a perfect demonstration of how both fearless action and slow caution are needed to save the day.
The Bears, Cavin, and Calla successfully holding off Igthorn and his mooks for an hour while all of Dunwyn is under a sleep spell, keeping every single one of them from getting inside the walls. The closest call comes when Cavin sees an ogre about to climb over a far wall with nobody nearby to stop him — Cubbi takes a drink of juice, jumps from rooftop to rooftop across the courtyard, and bounces between the wall and the ogre's head like a paddleball until he knocks the invader back over the edge. Finally, Igthorn tries rolling a wooden bridge up to get him across the moat, leading to a showdown between him and Calla, who's been struggling lately about feeling useless and sulking about being only a princess who can't do anything like a king does:
Calla: Your ogres won't get in here without a smarter general!
Igthorn: If Gregor had had a son, I might be worried about getting in there!
Calla: Well, he didn't have a son — he had ME! And in his absence, I say what goes, and what goes is YOU! Because I'm the princess!
After calling herself a princess with pride for the first time, she orders the Gummis to lower the drawbridge. They think she's crazy but do what she says... causing it to hit the end of Igthorn's bridge and catapult him into the woods, his brainless mooks following close behind him. Her mood lasts to the end of the episode, when she walks proudly down the staircase with Cavin on her arm, impressing the servant who saw her trip and fall trying to do the same thing earlier.
Servant: Why, Princess Calla, that was... perfect!
Calla: Of course... (starts spinning her crown on her finger like a basketball) ...I'm the princess.
Tummi tricking Igthorn and the ogres into the Great Gummis' ancient obstacle course in "Tummi's Last Stand."
Zummi gets two in "For Whom The Spell Holds." The first is minor and Played for Laughs — after Gruffi calls him an amateur whose magic could never compete with the Great Gummis, he learns a "locking spell" that he casts on Gruffi and refuses to lift it until the latter admits he's a great magician. The second is more serious — after relentlessly chasing a monster through underground caverns and over a terrifying cliff to get the Great Book back, he's captured by Zorlok, who eventually threatens to hand Gruffi and Grammi over to his monster/servant if he doesn't get the Gummi medallion. After thinking it over for a second, Zummi hands over the medallion without any fuss. Now able to use the Gummi magic in the book, Zorlok undoes the locking spell placed on him and prepares to leave... but Zummi taunts and insults him until the wizard gets mad enough to prove how much stronger he is by trying to kill them all with a spell... which backfires and zaps him instead. Because Zummi remembered something Zorlok apparently didn't know — that no magic in the Great Book can be used to harm a Gummi Bear.
The escape from the island as the volcano erupts in "My Gummi Lies Over The Ocean."
Tummi also deserves a mention for building an entire, perfectly seaworthy boat all by himself.
Tummi refusing to lose the Gummiberry sapling he and Gusto came so far to find in "Day of the Beevilweevils," even though it means risking falling to his own death. We the audience know this is no longer necessary, but it turns out to be what saves them all, as seeing one of the Gummi Bears risk his life to save a tree convinces the sentient trees of Fangwood Forest that they can trust them and agree to let them go.
The disguised Calla winning the competition to be her own bodyguard in "Girl's Knight Out." Instead of being furious like she expected, her father is impressed enough to admit she is strong enough to take care of herself.
Sunni showing up at the climax of "Rocking Chair Bear," despite being rapidly aged into a decrepit old lady, to save the others from Lady Bane and get her own lock of hair back, restoring her youth.
Grammi tricking the crowd into believing the elf's show is a trick and saving her whole family in "Never Give A Gummi An Even Break."
The mid-air battle to free the birds and save the castle in "Wings Over Dunwyn."
Zummi during the Grand Finale, braving his fear of heights to fly out over the fleet of Great Gummi ships and warn them that they're about to fly into Igthorn's clutches, while trying to avoid the boulders being flung by Igthorn's catapults.
A Fanon example but still a valid one; many fans believe that post-series, Cavin and Calla lead Dunwyn (and possibly the world) into a Golden Age. Not through military might, though both of them are skilled fighters. Not through great intelligence, though both of them are very bright. No; their greatest strength? Their kindness and strong sense of honor is what gains them the respect and alliance of the Gummis.