The end of "Big Appetite In Little Tokyo," when Velma gives her creation, Dogbot, to the brat kid who was competing against her in a science contest.
Daphne: That was real sweet of you, Velma.
Velma: Well, I may have given Dogbot a king-sized brain...(hugging Scooby) but he just can't match Scooby Doo's king-sized heart.
There's another scene before that. The gang have just found Shaggy after the GodzillaExpy's rampage, and he says "I guess this is it - time to turn me in" (at this point, everyone believes he turns into the monster when he falls asleep). The gang's response? They immediately refuse - no matter what, they are not going to abandon their friend. Dawwww...
In "Farmed and Dangerous", the gang hears Scooby and the six puppies at the bottom of a well. Shaggy is about to jump down and save his buddy, but is informed that underneath the farm, there is a spooky graveyard. Doesn't stop him. Also doubles over as a Crowning Moment of Awesome.
Shaggy and Mei Ling's first meeting in "Block Long Hong Kong Terror," when it's revealed they have the same Duck Buddy. A Ship Tease that gives you the warm fuzzies.
Shaggy: Like, who'd thought? Hundreds of miles away.
(They smile at each other.)
Upon deciding that regaining their lost fame isn't worth the trouble in "It's Mean, It's Green, It's the Mystery Machine", Andy and Mandy decide to reconcile with their brother Randy. Andy and Mandy also reveal that they're the ones who, once per year, deposit a flower at their late bandmate's grave, with both of them admitting that they idolized the man.