Lex Luthor was created in 1940, when mad scientists were a staple of comic books and pulp novels, and nearly every superhero's rogues gallery included at least one. Nowadays, the trope is generally considered a dated cliché, but Luthor has nonetheless stuck around, and he remains Superman's archenemy, with the writers devoting considerable effort to fleshing out the character's personality and motivations. One of the more popular reinventions was to make him a sleazy businessman who posed a threat to Superman due to his vast influence in Metropolis, respected public image and incredible wealth, which has become the most popular interpretation of the character. But as a nod to his roots as a mad scientist, most modern versions still portray him as a scientific genius who runs a tech company, and uses advanced technology to fight Superman—providing a plausible excuse for the two characters to go toe-to-toe.
Bizarro was originally a dimwitted clone of Superman created by a scientist's replicating ray, and he famously ruled over the topsy-turvy cube-shaped planet of "Bizarro World", which was populated by similarly dimwitted replicas of Superman and his friends. Some of the campier aspects of the character's origin story — like the cube-shaped planet, and the replicating ray — wouldn't have translated very well to the darker Post-Crisis continuity, but the general concept of a flawed Superman replica was popular enough that Bizarro was reimagined as a genetically engineered clone created by a team of scientists on Lex Luthor's payroll, and his mental deficiency was played a bit more dramatically, making him more of a Tragic Monster than a bumbling simpleton.
Originally, he was Superman, disguised as mild-mannered reporter Clark Kent. He really had no reason to have a human identity, especially after his powers increased to the point that the job at the newspaper in order to find out about dirty deeds was no longer necessary. Post-Crisis, he's now more Clark Kent who dresses up as Superman and not the other way around. It's also been said that he likes the Self-Imposed Challenge of learning to be good at something for reasons other than his super-powers.
There's also Superman's use of glasses to hide his civilian identity. Today, very few people seriously believe that he can effortlessly disguise his face just by donning a pair of glasses, but a few modern writers have toyed with the idea that he actually uses the glasses to hide his distinctive eye color (a bright shade of robin's egg blue that isn't seen in normal human eyes), which is one of the few visible markers of his Kryptonian heritage. Christopher Reeve's performance in the movies is also credited with making Clark Kenting a lot more plausible; with his acting ability, he was able to play Clark and Superman as two completely distinct characters, establishing that Clark also completely changes his voice, posture, and overall demeanor whenever he becomes Superman. This was enough to make pretty much anyone say "Okay, now I can see it."
By The '80s, Oswald "The Prankster" Loomis was one of the most problematic SupermanRogues Gallery villains because, for such an enduring character (he's one of the precious few still recurring Superman characters created back in The Golden Age of Comic Books) he posed the least credible threat of all: a gangster, his gimmick consisted in committing crimes in the form of pranks, without having any extraordinary powers himself. This made him the least threatening Superman villain fifty years later when John Byrne re-imagined him as a deranged former tv star bent on revenge for the cancellation of his show by Morgan Edge. This version still was not enough to convince the readers, but by then the Prankster had been around for so long and appeared on practically every Superman live action television show, so he was difficult to get rid off. Thus, in The Noughties he was again retooled as an arms dealer who also specialized in creating diversions to stall Superman when another more important crime was being committed by the Prankster's clients. Still not happy with the result, during the New 52 the Prankster was again re-imagined but as a villain for Nightwing, this time he appeared as a computer expert bent on avenging his father's death due to the carelessness of the corrupt mayor of Chicago.
Power Girl's Cleavage Window has gotten DC Comics many complaints of sexism over the years, since it pretty clearly just exists to give readers something to ogle. It probably wouldn't fly if the character were introduced today, but it's also such an iconic part of her costume that it looks strange without it (partly because she doesn't have a chest insignia to replace it). The artists have tried to redesign her costume many times to get rid of the window, but none of their attempts have stuck. Eventually the writers settled on making Power Girl an unapologetic showoff with a playfully flirtatious personality, so it actually seems (somewhat) in-character that she would show off her breasts for the sake of it. It helps that she also has a healthy sense of humor about it, and isn't afraid to hang a lampshade on her sex appeal.
Supergirl's origins in The Supergirl From Krypton (1959), where she was raised in Argo City which survived the destruction of Krypton, were confusing to some creators. The Supergirl from Krypton (2004) simplifies her backstory by having her leave via a rocket like Superman, except that the rocket went off course, arriving at its destination years later. The technology of the rocket kept her in an unaging stasis, thus while she is chronologically older, she is physically younger. More modern interpretations focus more on the Child of Two Worlds aspect contrasting her perspective to the Earth raised Superman.
In a rather ironic case of Celebrity Paradox, Brainiac's name began to come off as a bit ridiculous after the character had been around for a decade or two, as the term "brainiac" eventually entered the popular American lexicon as a juvenile slang term for "genius" (the character is actually the origin of the word, which was coined simply as a portmanteau of "brain", "maniac", and "ENIAC", the first programmable computer), making one wonder why an alien robot would unironically call himself that in-universe. Some Post-Crisis comics retroactively decided that his name was an abbreviation of "Braininteractive construct", so it was a bit easier to take seriously.
Krypto the Superdog was one of many animal sidekicks introduced during the Silver Age of comics -in "The Super Dog from Krypton". He would go on adventures with the other Kryptonians and had a thought process like a human. After Crisis on Infinite Earths and DC's mandate that Superman be the only surviving Kryptonian various substitutes for Krypto were created but none of them stuck. Eventually the mandate lessened on Krypto came back, but by then DC has moved away from goofy animal sidekicks. So instead writers emphasized his dog nature, making him act like an actual dog with a dog's temperament and loyalty to his masters, and usually hangs around the Kents.
The infamous "Superman Blue" incarnation of the title character — where in 1998, Clark Kent was reimagined into becoming a blue and white-costumed Energy Being with electromagnetic powers, who also gained a separate clone named "Superman Red" (and was itself a reimagining of a Silver Age what-if comic attempting to shake up the status quo) — only lasted for a year before being reverted, and has largely been buried by modern DC as an embarrassing and unnecessarily drastic reinvention. However, several creators have toyed with preserving some of the attempted redesign for newer characters, paying respect to the failed, but interesting experiment and making it more palatable within the DCU:
Sharon Vance, aka "Strange Visitor", was introduced in 1999 (just a year after Superman Blue was canned), and built on a similar premise. After being struck by lightning and merging with a cosmic entity, Vance gained a containment suit designed in almost the exact same scheme as that of Superman Blue's, as well as gaining a similar set of electrical superpowers, becoming an occasional supporting character for Supes until her Heroic Sacrifice in Our Worlds at War.
2023 saw Clark's son, Jonathan Kent, the official second Man of Steel, once again also developing his own energy-based superpowers, regaining a very similar blue-and-white look once used by his old man.
that isn't seen in normal human eyes), which is one of the few visible markers of his Kryptonian heritage. Christopher Reeve's performance in the movies is also credited with making Clark Kenting a lot more plausible; with his acting ability, he was able to play Clark and Superman as two completely distinct characters, establishing that Clark also completely changes his voice, posture, and overall demeanor whenever he becomes Superman. This was enough to make pretty much anyone say "Okay, now I can see it."