Overall, Wingus's decision to be exiled from his species because of his refusal to have Joe removed from his feet. Keeping him safe and fed, then watching him grow up to be strong and stomping all the troubles away. It just goes to show how much the little guy cares about his 'other-half'/friend. And it also shows why you don't mess around with them.
Joe: "You gave up your life to help me. At least now you can become King Super Bird or whatever."
Wingus: "Only a true friend would sacrifice himself for another."
And this little bit, even though it's short:
Joe: "You helped save me so you could keep playing 'Poke The Mayor', right?"
Octocataclysm: After Mister Smarty Smarts's latest plan to take over the island fails, Octocat decides to do it herself and used mind-control collars to brainwash the other mutants into doing her bidding. At the end of the episode, we see that she was using them to build a giant statue of Smarty Smarts and herself. D'awwww.
Of Masters And Minions: Smarty Smarts and Octocat's reunion at the end of the episode. Even the other mutants (who normally despise and/or are terrified of the two) appear to find the scene touching.
The episode Same Differance gives us two: The first one is when Joe decides to rescue Peri and Entrée from being trapped in a giant pretzel forever, despite the fact that they constantly make his life a living hell. The second is when Smarty Smarts and Joe meet up in the end of the episode, and agree that even if they're techically enemies they can still hang out (before getting into a fight about whether or not lemonade and lemon juice are the same thing).
Pretty much the entire plot of Honorary Freak. Getting past all the show's regular insanity, it all comes down to Patricia feeling sad and lonely for not being a mutant, and Peri and Entrče trying to cheer her up and reassure her that she's one of them, no matter what she is. Now that is touching.