Superman is a hero with a wide variety of bizarre and wonderful enemies who can present challenges of all kinds. Despite this enormous catalogue, the live-action translations of the source tend to focus on a couple main nemeses; the most popular of which clearly being billionaire super-genius Lex Luthor.
Alexander Joseph Luthor was introduced just under two years after Superman's first appearance. Early on, he was a fairly typical evil businessman, engineering massive tragedies for personal profit and being foiled by Superman. As he developed, his connection to Superman became hateful and obsessive. The current take on the character sees him despise the hero, motivating him to kill and replace Superman as a benevolent ruler of all mankind.
Atom Man vs. Superman (1950)
Much like Batman, Superman was also featured in a number of film serials before he was revitalized on-screen in the 70s. One of those was Atom Man vs. Superman, which marked the very first appearance of Lex Luthor in live-action. Played by Lyle Talbot, this version of Lex Luthor was essentially a prototype for the character, using his intellect to threaten Metropolis with various inventions.
Superman: The Movie (1978)
The Richard Donner Superman series is a masterclass in classic superhero film. Award-winning actor Gene Hackman portrays Luthor in three of the four films in this series. This Luthor is more of a comedic foil to the hero, engaging in wacky schemes for profit.
In the first film, he is the primary antagonist, planning to bomb the San Andreas fault to sink California in order to transform some of his real estate holdings into beachfront property. In the second, Luthor plays bumbling sidekick to Zod, failing to mislead Superman and being recaptured for his trouble. In the much-maligned fourth film, he combines his DNA with some of Superman's to create Nuclear Man, the film's main antagonist. Hackman's Luthor is a fun villain who manages to pose a massive threat while remaining lighthearted.
Superboy (1988)
This TV series does not focus on Connor Kent, the character typically associated with the name Superboy today, but instead focuses on Clark Kent in his youth. This iteration of Luthor is portrayed by Scott James Wells, then by Sherman Howard in following seasons. Luthor attends college alongside Clark Kent and schemes to best him at every turn. In the first season finale, Kent saves him from a lab fire, accidentally resulting in his premature balding.
Luthor subsequently goes completely insane and begins a campaign of murder and corporate sabotage with the end goal of killing a former classmate. Oddly enough, when his backstory is revealed, it's comparable to his Post-Crisis origin revealed in the comics after the show's conclusion. This Luthor acquires his wealth after an insurance payout, which Luthor gains through killing his parents.
Lois & Clark: The New Adventures of Superman (1993)
As much a domestic romance narrative as a superhero action show, Lois & Clark features a ton of strange alterations to Superman's source material. The series explains that Luthor is the third richest person alive, and sets him up as antagonist to Superman and Clark Kent. He actually dies at the end of the first season after his corruption is exposed to the public, but is later resurrected.
This Luthor, portrayed by John Shea, is a scheming supervillain who wields clones, kryptonite, mind-swapping technology and much more to try to defeat his bitter rival. This Luthor is also consistently targeting Lois Lane, either to get closer to Superman or for more romantic reasons.
Smallville (2001)
Another series based around Superman's youth, Smallville is the longest running series about the character thus far. Lex Luthor is here portrayed by Michael Rosenbaum, in what is probably his most in depth portrayal at the time. Smallville ran for 10 seasons, and in that long narrative path, fans witnessed Lex evolve into the villain they know and love. Lex meets Clark Kent in a unique way, plowing his car into the young superhero and being saved from certain death by Kent's powers. The pair form a friendship that degrades over time as Luthor succumbs to his worst influences. Luthor shifts from questionable to outright evil as obsession with Superman takes him over. This version of the character is a deep exploration of the psychological journey taken by Luthor, and the grim surroundings he grew up in, which led logically to his place in the future.
Superman Returns (2006)
Kevin Spacey takes on the role in 2006's Superman Returns, a direct continuation to the original Richard Donner series of films, but makes the character more serious and violent. Facing off against Brandon Routh's Superman, this version of Luthor is much more calculating and nefarious. He also comes very close to defeating Superman once and for all by using science to create an entire island out of Kryptonite. Of course, even this isn't enough to deter Supes, as he lifts the entire island out of the ocean and hurls it into space.
Batman v Superman: Dawn of Justice (2016)
Jessie Eisenberg's performance as Luthor in the modern DCEU has gotten some very mixed reception. Eisenberg portrays the character as a fast-talking, Silicon Valley, modern take on a tech mogul. He primarily appears in Batman v Superman, but also shows up in the end credits scene of Justice League. His role feels fairly omniscient, he discovers both Superman and Batman's identities, monitors the existence of other metahumans throughout time, and much like Nuclear Man in Superman IV, he mixes his blood with Zod's to create Doomsday. This take on Luthor is consumately evil and intelligent to the point of humor. Nearly every aspect of BvS' plot progression is pushed forward by Luthor, down to the title fight, and he ends the film behind bars, clearly aware of some upcoming cosmic threat.
Supergirl (2015)
Lex Luthor is here portrayed by Jon Cryer, who incidentally portrayed Luthor's nephew in Superman IV. Luthor becomes the main antagonist of season four of this Arrowverse series and subsequently crosses over with the other works in that TV universe. Cryer is a ton of fun as Luthor, he brings a great deal of charisma to the villainous character. Like Smallville, Luthor went from friends to enemies with Clark Kent, then began a lifelong vendetta against all Kryptonians. This Luthor jumps between universes, travels through time, gets elected to high office, and wields the phantom zone against his enemies. He's the most powerful form of the character thus far, but his current fate sees him trapped in the Phantom Zone with no clear way out.
Lex Luthor is Superman's best-known adversary and he is sure to pop up in many future iterations. Fans can catch him in his teased appearance in the next season of Titans and his DCEU or Arrowverse iterations could reappear anytime, possibly with a new star.