Although he has had many, many awesome moments before, Superman had been off the big screen for 19 years before he returned in, well, Superman Returns. It was of crucial importance that Superman did something spectacularly awesome, and he did not disappoint: he is shot with several hundred bullets from a minigun by a Mook, followed by the Mook getting off the minigun, pulling out a pistol and firing point-blank into his face. The bullet bounces off Superman's eye. The Mook looks horrified. Superman smiles. And the crowd cheers as Superman wins the fight merely by showing up.
Supes' first helicopter-grabbing appearance in the first movie, and its recapitulation in Returns, are both fittingly awesome.
His first public reappearance. He saves the Space Shuttle, a jet full of innocent people and reporters, and Lois, and then politely admonishes them that flying is, statistically speaking "still the safest way to travel." Then he stands in the doorway. The crowd goes wild. And because it was a televised game, the entire city gets to see it and also cheer with great enthusiasm. All while his Theme Tune is playing for the audience. Oh, yeah.
It's even more awesome when one realizes that one of the first people to start cheering is a little kid. In-Universe, Superman had been missing for five years so the kid very likely had never seen him before or, if he had, didn't remember anything about it. However, the parents probably told him enough stories about Supes for the kid to be able to recognize him at first sight.
There's also the scene where Lois and her family are trapped in the galley of a sinking ship, with a mournful dirge playing. You see their despairing faces through the portal as they struggle hopelessly against an inescapable doom. And that is when you see two red boots land on the window as the Superman March starts into full thunder and Superman saves the day!
The airplane rescue was good, yes, but Superman lifting an entire friggin' ISLAND that's laced with Kryptonite takes the "awesome" crown. The epic mix of the Superman theme, Luthor's Oh Crap moment, and the Death Glare Superman gives him as he flees.
When Lois Lane's five-year-old son saves her from a mook BY THROWING A PIANO AT HIM. Thereby revealing who his real dad is.
Lois' Muggle love interest deserved a CMoA award for his response when Lois gets the fax-machine message to the Daily Planet. Does he run whining for help? Does he sit around waiting for Supes to show up? Does he angst about the fact that he doesn't have super-powers himself? Nope, he just gets up and goes to rescue them anyway.
There's also a subtle one when Lois demands they go back and rescue Superman. Keep in mind they're facing heavy winds, jagged rocks, and possibly people with guns. Richard considers it for only a second before he says "okay" and turns the plane around.
A CMoA for Richard comes when he takes off the seaplane— this time without Super-help— thus doing what he previously thought couldn't be done.
Superman Returns manages to pull off a CMoA in the opening credits. The epicness of the eyecandy plus John Williams' rousing theme is awesome.
Heck, same goes for the original 1978 movie, too; you know you're in for a treat when even the opening credits are epic.
Superman is flying and remembering the words of his father:
Jor-El: "They can be a great people, Kal-El, they wish to be. They only lack the light to show them the way. For this reason above all, their capacity for good, I have sent them you... my only son."
The combination of music,visuals and dialogue is just about perfect. Siegel and Shuster would be proud.
Superman gets a small but important one during the scene when he on the receiving end of a truly brutal beatdown from Lex Luthor and his thugs. As he is being dragged away, one can hear him let out a defiant cry of "I'm still Superman!" Even without his powers and when evil is all around him, he is still a force for good and will never give that up. If there was ever any doubt that Singer loved this character, it disappeared with those words.
The entire sequence wherein Superman saves Metropolis before heading off to Lex at the island. Sure, other superheroes have cities to save on a regular basis, but no one quite does it like the original.