In Crash Nitro Kart, Team Bandicoot is confronted by boastful tribesman Krunk, who insists their Earth is a copy of Terra. After defeating him, a visibly dejected Krunk accepts his loss and offers them the world key as promised. Feeling bad, Crash offers him a gift in return; the yoyo he is constantly seeing playing with in his idle animations in the series.
Krunk: What is this?...Gift from your world?
Krunk: Thank you...I am sorry. We actually copied your planet.
*Crash snickers as Krunk attempts to work the yoyo.*
The other rivals have similar if more understated moments with the Bandicoot team. Coco similarly feels sorry for Nash, programmed to constantly stay awake and on edge, and hacks his brain to take some shut eye ("looked like he needed some, the poor shark thingy"). Big Norm, despite boasting before the match, proves a surprisingly good sport and tells them they make a great team. Even Velo ultimately befriends Crash after his true form is revealed and sends them back to Earth willingly after he hands him back his power.
It's a subtle villainous case, but this game also establishes Tiny's Undying Loyalty to Doctor Cortex. He's a clumsy simpleton, but he cheerfully follows (as in tries to) his master's every command and the moment a challenger such as Nash threatens the doctor, he runs in front furiously guarding him. The fact the animation is complex enough to give Tiny Puppy-Dog Eyes helps.
An understated one, but when the bandicoots are first abducted, Crash checks out his position and then wonders where the others are. He then turns to see Crunch and Coco, the latter of which is bouncing up and down waving happily at finding him.
The ending to Crash Of The Titans, after finally saving Coco and earning a hug from his younger sister. As deranged as the story and dialogue were for that game it earns points for developing a Big Brother Instinct for the usually brainless bandicoot.
Coco: You did it Crash! Thanks, Big Brother!
Cortex: Oh gross. Get a room.
Let's not forget the group hug between Crash, Coco and Crunch after they make it back outside. It really speak volumes about Crunch's dedication to his Heel–Face Turn when he's sharing a warm and loving hug with the people he was fighting just a few years earlier...Though Coco kinda ruins it by mentioning that he smells like bacon...
And later, Cortex's So Proud of You moment with Nina. Since betraying him was the most evil thing she'd done. For that he saved her from the crashing Doominator. It's almost undone right after however but Even Evil Has Loved Ones.
Cortex: I'm still going to spank you stupid for this!
At the end of the first boss, Crash and Aku are set to chase Cortex to his lair, though Crash is worried over the exhausted Yuktopus. Aku states he'll be fine before the Yuktopus makes a salute at the two.
Pasadena establishes herself as a rowdy competitor to the main cast in Crash Tag Team Racing, and maintains that disposition in most of her game play dialogue. Whenever Crash talks to her however, she instantly becomes The Cutie and shows (perhaps a bit too much of) her gratitude for whatever favors he provides.
Pasadena's only interest in winning the course is so her boss can keep his beloved park. When the bandicoots win the park and see how upset Pasadena is over Von Clutch's Disney Death, they instantly give it back to Von Clutch as well. Upon his resurrection, Von Clutch is so overjoyed at the success he gives the bandicoots free lifetime passes and goes into an adorable happy fit (Crash ruins the moment by patting out his power gem however).
While Crash Purple/Fusion was a pretty lackluster crossover, the final image of Crash hugging Spyro during the credits is pretty adorable.
They have a similarly heartwarming hug scene in the Skylanders Academy cartoon.