Sakura rollerskating up a wall then jumping onto the runaway Fly card in the first episode. It was the only idea she had when Fly was chasing her and Kero down. Then she instinctively summons Windy and utters a command to incapacitate Fly and seal it. No wonder Kero said she was the Card Captor.
"Sakura's First Heart-Racing Date"
Though it doesn't go well, the penguin's first instinct when its trainer is trapped is to go over to help free her from the whirlpool. Brave little guy.
Touya ends up saving the trainer and the penguin when she calls for help and explains they're caught. We find out later that he had powers, meaning he knew what he was dealing with without missing a beat.
Watery tries to fight dirty and flood the restaurant where Sakura and Yukito are getting a meal. It then succeeds in trapping Sakura underwater, and she can't summon the wand while holding her breath. Who comes to the rescue? Yukito! While underwater, he finds an ax and breaks down the door, draining the water. This allows Sakura to surface.
When Yukito and Touya talk about ice, Sakura gets a "Eureka!" Moment on how to seal the card. At night, she goads it to come after her. Then she flies into the freezers, unleashes Windy, and closes the doors. Cue Watery becoming a block of ice.
The Whac-A-Mole game from episode 40, the Dream Card episode. Sakura was struggling to hit all the moles coming from all around her, so Meiling decided to grab a hammer and help her out. With each other's backs covered, they had the time of their lives smashing up moles. Especially awesome is that Meiling used to hate Sakura with a passion and constantly distrust her when they first met, but at that moment, they were playing together like they've been best friends forever.
Against the Twin Card, Syaoran and Meiling's perfectly synchronized attack was the greatest display of Badass Normal in the whole series.
The second greatest being Meiling vs the Fight Card.
Meiling during the episode when Sakura is forced to transform The Freeze; not only does Meiling manage to stop a good deal of the large stone/metal penguins with just her bare hands to protect both herself and Sakura, but it's her idea to use The Freeze in the first place. Later, her very selfless and very immediate I Want My Beloved to Be Happy moment, a huge leap from the Clingy Jealous Girl that hated Sakura that she once was.
Tomoyo using her singing prowess to help capture the The Song card is a unique case. She similarly does this to help convert The Song into a Sakura card later on.
Also, how Sakura caught The Jump. Specially because at some point the girl (who mind you, was still a Naïve Newcomer and basically realising how the deal worked) summons The Fly while taking a huge fall and being upside down. A little mistake and she would've died, but she managed to get this perfectly done.
"Sakura And The Last Judgement"
With the risk of applauding assault against a minor, The entire Last Or Final Judgment. Poor animation aside it was one of the most brutally actioned scenes in the anime.
Syaoran to his credit is a Curb-Stomp Cushion. He relies on his natural magic to deflect Yue's initial attacks, while the being says that unless he uses a Clow Card, he's toast. Still, he's doing well until using Time to stall. Unknown to him, Time is under Yue's domain.
Sakura on seeing Syaoran paralyzed says she needs to help him, and bangs at the barrier which Yue created. Syaoran, on seeing Yue hit Sakura with shards of ice, shouts, "THAT'S ENOUGH!" and prepares to charge when Yue tests her in turn. It's only Cerberus telling him that if he interferes then Sakura loses by default that Syaoran backs down.
Kaho using her Moon Bell to save Sakura from the world where everyone has lost their most precious feeling. Yue tries warning her that she'll be cursed, but Kaho says screw that, she uses the power of the moon as well.
A meta example: NISAmerica managed to rescue it. They're giving it the full blu-ray remastered treatment. Best of all, they're using the Animax dub, which, according to Madman Entertainment, is supposedly EXTREMELY taxing and hard to get (even though it's in mono only). That takes massive balls and guts to do. They must really love this show if they managed to give it this much royal treatment.
Syaoran's mystical entrance at the very end shot of Episode 7. From now on, the series will not be the same...
In the anime, Syaoran serves as a more Worthy Opponent to Sakura, earning a dozen or so cards himself prior to the Final Judgement. Seeing him use some of the cards effectively is likely gratifying to his fans from the original manga. Sakura sometimes sucks the sport out of it by outright letting him have the card however, in which case it becomes a Heartwarming Moment. Syaoran also returns the favor to her sometimes.
Syaoran has a recurring tendency for pulling acts that are noted shouldn't be possible with his magic level. Yue notes his surprise he managed to overpower both Maze and Illusion in Episode 66. Punctuated since these are nearly always to protect Sakura.
Whenever Sakura transforms a card counts. Not only does signal awesome to come but it means she is becoming a more powerful mage. The incantation is also awesome. "Card originally created by Clow, abandon your past appearance and transform. I command you as your new master!" It is not often hears Sakura speaking so assertively, which makes it all the more notable.
Sakura defeating Eriol's final test, bringing sunlight to Tomeda so everyone will awaken from their otherwise permanent slumber, and converting all of her remaining cards in the process. Bonus points for Kero and Yue taking form inside her wand to empower her.
Syaoran, despite being affected by the spell, manages to stay awake throughout the entire thing, despite weakening himself to save Sakura from an attack and helping her with the load of her final spell. Oh, and he finally spits it out.
The fight against the sentient railing in Episode 61 is one of the more intense tests in the final arc. Extra props because it's the nearest Syaoran gets to actually using his sword properly, with Sakura's staff working just as effectively.
The opening to the 2nd movie with Sakura slicing through a earth monster with Sword, Keroberos fending off a fire monster, and Yue calmly destroying yet another one is made of sheer win with the music on top of it adding the feel. Then it turns into a Funny Moment when it is revealed it's actually a video and performance staged by Tomoyo.
The sheer fact Sakura fully dealt with every troubled soul and every antagonistic force, just by being nice to them. Everyone in the cast by the end of the series is her loyal friend.
Kero shows Sakura how she can heal an injured Fly, by writing her name on the card and placing it in the Clow Book.
Tomoyo of all people saves Sakura when Watery goes after her and Chiharu in the elementary school pool. Sakura managed to free Chiharu, but Watery proceeded to send her through a whirlpool. We don't know how it went down, due to Watery knocking out Sakura, but the other girls are impressed and Tomoyo modestly says she doesn't swim well.
The fact that Watery got the jump on Sakura. Kero notes that Sakura is a great swimmer, so her nearly drowning is unusual.
When Illusion tries drowning Sakura, by posing as her mother, Kero immediately tries to fly into the lake where she's investigating. Cue him getting zapped. Tomoyo calls for him and starts to climb over the railing. Someone beats her to the punch: Yukito. He pulls Sakura up and takes her to his grandparents' house to recuperate.
Illusion then grabs Sakura, who flies to talk to what she thinks is the ghost of her mother. She starts drowning but remembers Yukito saying that her mother would never want to hurt her. Cue Sakura breaking free and getting to the surface of the lake.
Syaoran's first response to a brainwashed Rika attacking Sakura; blocking the blade before Sakura can get stabbed. He's all prepared to fight before Sakura says that he can't hurt Rika and she knows what to do. Cue her summoning Illusion, and knocking the Sword card from her hand.
Yamakazi sees that Syaoran is intimidating Sakura on learning Yukito cut her hair. He lifts the kid like a ragdoll, much to Syaoran's bewilderment. When seeing they have a score to settle, Yamakazi tells them that badminton, the next sport in recess, was used to handle honor duels. Syaoran believes it, and backs off to challenge Sakura later. They end up tieing.
During the Last Judgment, Sakura breaks free of Wood's vines when Yue turns them on her, unlike in the anime where they successfully smothered her. Yue even commends her for that, saying she's more powerful than he thought.