The episode where one of the Tachikomas helps a little girl find her lost dog. It didn't have to help her, but it did.
The last scene of the first episode of season two, when the Tachikomas return. The look on Batou's face really said it all.
Earlier in the episode, in order to convince the Prime Minister to allow Section 9 to solve a hostage crisis, Aramaki offers himself up as the fall guy in case any of the hostages die. This shows the kind of faith he has in his team - he bets his own freedom that they will succeed. Which, of course, they do. They're Section 9.
The episode Affection in season 2 may be the most touching bit of backstory ever conceived. Kind of makes you hope that the Boy and Motoko find each other.
A nurse friend of the Major's tells her of someone stealing human hearts. She is so enraged that she pretends to be Yakuza, hunting him down to cut him up on the pretense of him competing with big criminal business, but in actuality because she is so upset at the crime.
Just about anytime Batou's insanely obvious fixation (*coughcrushcough*) on The Major appears on all of its obvious glory. It seems to happen at least once per season. In season 1 we have him wailing a sufferingBig "NO!" when he thinks that the Major has been killed and in season 2 he runs into a warzone to prevent the Major from dying. Even nicer is that while talking to Kuze the Major implies that she's not completely alone and that she in fact has someone to talk to. Cue Batou appearing. Their relationship, while subdued, is about the most normal we see this two, extremely normal individuals, do.