The final scenes are just made of this, particularly this speech:
Stitch: This is my family. I found it, all on my own. It's little...and broken...but still good. Yeah. Still good.
Fridge Brilliance: Remember what the Grand Councilwoman said at Stitch's sentencing, when determining whether he was a monster? All he ever had to do was show that there was "something inside (him) that is good."
Which is especially amazing because when they finally corner Stitch, who has been seen in the eyes of the Galactic Federation or whatever to be an irredeemable little monster, he simply stands up and talks to them. His only questions are if he has to leave, and if he can say goodbye. Just... * sniff*
The final photo at the end of the first film: Rather than it only being Lilo, Nani and their deceased parents, another photo is partly overlapping it now, so it looks like Stitch is sitting with them.
The entire ending credits, plus photo montage with "Burning Love" in the background, could be seen as one long CMOH: It depicts Lilo's shattered family not only whole again, but bigger and happier than ever before.
On that note... This troper isn't sure how much she liked the sequel, but the ending... She has to admit to having teared up. "Stitch not bad. Stitch fluffy!" Uwaah!
The short film "The Origin of Stitch" is just one big heartwarmer, particularily when Jumba hugs Stitch just like a father would. Awwww...
The frog, seemingly nothing more than a Brick Joke. But when Gantu makes his strafing run, the frog jumps on Stitch's head while eyeing Gantu's ship, giving the impression he's trying to shield Stitch from the attack. Which Stitch repays by saving him.
The montage of Lilo, Nani, David, and Stitch at the beach that plays during "The Hawaiian Rollercoaster Ride". Considering how many difficulties Nani, Lilo, and Stitch have been going through, seeing them all having fun together is very touching.