In Amethyst, Princess of Gemworld, Lady Mordiel captures a peasant girl with a small fraction of blood power, and after talking to her casually, murders her to absorb her fragment of power; then she orders the girl's family to be suitably compensated.
Batman first appeared on a rooftop beating up thugs.
Cassandra Cain throwing herself in front of Commissioner Gordon to prevent him from being shot by an assassin whom we later learn is her father. She swiftly becomes the new Batgirl, with Barbara Gordon's blessing and gratitude.
In Grayson, Dick's use of a gun as a batarang in the opening pages of the first issue makes it clear that this is still the same Dick Grayson that fans love.
Flag: Are you out of your cotton-picking mind, lady? Waller: Frankly, I couldn't be more serious, colonel! And by the way, if you ever again call anything about me 'cotton-picking,' mister —- I'll stuff those bright, shiny eagles on your shoulders so far up your butt, they'll be able to nest in your skull!
Superman himself in the cover◊ of Action Comics #1: He lifts and smashes a car into a rock, displaying immense strength which scares a group of thugs out of their wits.
In her very first appearance Lois Lane: reluctantly went out on a date with Clark, got annoyed that Clark didn't stand up to a mobster that was bullying them, slapped the mobster herself, got promptly kidnapped by the mobster, and was rescued by Superman. A rather good overview of what her life would be like for the rest of her existence.
Supergirl's first appearance in "The Supergirl From Krypton (1959)" has her agreeing with Superman's plan to not use her powers without permission and then using them anyway as soon as her cousin's back is turned.
Supergirl (1984): Selena's first scene involves one conversation where she reveals within two panels that she is a short-tempered, impatient witch with world-conquering ambitions, she yearns for more power, and she dislikes coming across as sweet or kind.
In her first appearance, Power Girl plugs a volcano, takes up the "Power Girl" name because "it won't confuse [her] with [her] cousin" and makes Wildcat and Flash feel redundant within two pages.
In crossover "From Eternia— With Death!", which is the first Masters of the Universe story, Skeletor praises Superman out loud for being perceptive enough to realize that he couldn't care less for his underlyings' well-being. Later, upon being defeated, Skeletor teleports away as swearing revenge, and He-Man confirms his nemesis has made a habit of it.
Doom Patrol: In a 1965 comic, Beast Boy invaded Doom Patrol headquarters and ransacked everything (up to and including defacing a picture of Elasti-girl and putting an axe through one of Robotman's spare head units), came back the next night and got caught only when the Doom Patrol successfully ganged up on him. When they finally let the teenage punk out, he immediately started bellowing at them for messing up his hair and shoes and started another fight, hurling insults in every direction. He then had the gall to demand they let him on the team. The Doom Patrol hated his guts, but the fans loved him, and he's been around for more than fifty years since.
Rorschach's opening narration provides a glimpse into his unstable mind: a retired crimefighter who now believes the city deserves its problems and longs for the day when the people are desperate enough to want his help again... just so he can smugly refuse.
Wonder Woman: Diana rescuing Steve Trevor from his crashed plane despite not knowing who he is and helping to nurse him back to health. As well as defying her mother to join the contest to determine who will be her people's representative to Man's World.