As cheesy as Superfriends was, there was one powerful moment in "Universe of Evil" when Superman is trapped in a "Mirror, Mirror" version of his world, hunted by the Super Enemies and authorities. Desperate, he seeks out a scientist in a desperate plea for help to find some means to get back home. When the frightened scientist demands he prove his strange story is true, Superman admits he cannot and leaves her to judge whether she can believe him. The scientist comes concludes that an evil person would never place such trust in another's judgment and wholeheartedly offers her help without a second thought. After they devise a plan, she has only one request, that Superman come back to free her world and he tells her she can count on him returning in force. At the end of the story with Superman safely home, he says he intends to keep that vow to his new friend to free her world, and the Super Friends immediately agree to join the invasion.
One of the All New Super Friends Hour health PSAs has Superman landing to talk to a young boy walking on a lonely road, abandoned by false friends when he wouldn't partake in narcotics. There is a charming simplicity of the Man of Steel, who is looking out for the world, taking the time to help a lost child paying the price for having a conscience by simply telling the boy he did the right thing and flying him home.
There's a great moment in a Wonder Twins solo story called "Prejudice." In this story, a black man is being chased by two racist hoodlums and they find themselves in a construction site's building girders at a significant height. The hoodlums trip and find themselves both hanging from a girder in very real danger of falling to their deaths. Despite the fact that they had been threatening him, the black man comes back to try to save them. When one of the hoods asks in astonishment why, the black man says as he is struggling to pull them up, "Because we're all brothers, no matter what color we are!" While he is not able to prevent one of the hoodlums from falling, the black man is able to delay that for the critical few seconds the Wonder Twins need to rescue them.
In one episode, Wonder Woman was mind controlled by space pirates and Superman has to fight her. When she snares him with his magic lasso, he manages to snare her as well and asks her one question, "Are you my enemy, or my friend?" At that, the truth of her friendship sets her free.