Lex Luthor is Superman's ultimate Arch Enemy and typically uses his brain against the Man of Steel's brawn, carefully avoiding any actions that could make Superman be justified in attacking him. To the point where only the muckraking Clark Kent, not Superman, can even put a scratch on Luthor. In Infinite Crisis, Alexander Luthor Jr. (son of a heroic alternate universe Luthor) eventually becomes convinced that one of the few things every universe has in common is that the resident Luthor and Superman (or Superman analogue) will always be archenemies.
After Luthor, Brainiac comes in a close second, being one of the oldest villains in the rogues gallery, and certainly one of the most evil. He can match Superman blow-for-blow, shows up constantly, is feared by all Krytponians regularly endangers the world or even the multiverse, holds a Kryptonian city hostage, and recently killed Jonathan Kent. As one writer pointed out, he's the alien Superman isn't, an evil otherworldy invader instead of a messianic refugee.
General Zod is the Arch Enemy of Superman's father Jor-El, the one responsible for stopping his coup and imprisoning him in the Phantom Zone, with Superman inheriting the grudge. Following Superman's defeat of Zod in Last Son and the events of New Krypton, the rivalry turns very personal for the both of them.
While he could be seen as the Big Bad of the whole DC Universe, Darkseid definitely could fit this role for Superman, as he's the one villain bad enough to push Supes into a homicidal rage.
The Ultra-Humanite was originally designed to be Superman's arch-enemy - brilliant mind in a crippled body contrasting to the incredible physical might of Superman - but many of his traits were absorbed by fellow Mad Scientist Lex Luthor, and Ultra-Humanite rapidly faded from Superman's Rogues Gallery and became a more general villain for DC.
Post-Crisis Supergirl has Reactron. Over the course of both her solo series, and the New Krypton crossover, the two clashed repeatedly, leading to Reactron's murder of Supergirl's father, her mother Alura's Cold-Blooded Torture of Reactron upon his capture, and the eventual destruction of New Krypton when Reactron blew up himself, the planet, and Kara's mother. For both of them the conflict was always personal.
The Joker is Batman's Arch Enemy. His insanity and chaotic nature are the complete opposite of Batman's rigidly, even obsessively ordered intelligence. Though it's also their similarities. Both were shaped by great tragedy and loss (at least in the Joker's most commonly accepted origin story). Many people have said that Batman is just as insane as The Joker, he just manifests it in a different and more positive way and keeps control over it. The Joker himself has pointed this out numerous times and in many adaptations.
Ra's Al-Ghul has a great deal of respect for Batman, may be even more dangerous, and a far larger scale threat, than the Joker, and is the father of one of Bruce's main love interests. If not the Arch Enemy, Ra's is definitely the main Big Bad of Batman's enemies.
Two-Face was once a great friend of Batman's, and is a personification of his failure. He's also got an ugly relationship with all of the Robins.
The wrathful vengeance of Doctor Doom will never be sated! Never — until the earth runs red with the blood of that accursed REED RICHARDS!!
The rest of the Fantastic Four as well, to a lesser extent. After he crushed Doom's hands, the Thing also jumped pretty high on his list.
Sinestro is Hal Jordan's Arch Enemy; similarly, the Green Lantern Corps treat the Sinestro Corps as their most dangerous opposing organization (even though the Red Lanterns have the potential to go on homicidal rampages if left unchecked).
Wonder Woman's is generally Circe or Cheetah, depending on who's writing. Ares gets in on the act too. He was, after all, her original Golden Age arch enemy, and is the biggest bad in her rogues gallery. As of Flashpoint Hera may be stepping into the role.
Depending on continuity the reasons behind Arthur and Orm's rivalry differs. But it usually revolves around the two brothers fighting over who is more fit to lead Atlantis. With Black Manta, their relationship is just full of mutual hatred.
Deathstroke the Terminator is Robin/Nightwing's Arch Enemy. Of all the Titans, Slade hated Grayson the most. Whenever Slade and Grayson were in the same fight, regardless of how many others were involved, they nearly always went after each other. This animosity was ramped up immensely when Slade orchestrated the destruction of Blüdhaven, Nightwing's "Gotham" so to speak, and, when he, even more recently, cybernetically hijacked Damian Wayne's body in an attempt to kill Grayson. Deathstroke also harbors a grudge against Grayson for "stealing his kids" from him
Shazam: Things get interesting here, and a little complicated. Billy/Captain Marvel has usually considered Black Adam or Dr. Sivana to be his worst enemy. Freddy/Captain Marvel Jr. considers Captain Nazi, who killed his grandfather, to be his worst enemy. However, the archenemy of the Marvel family as a whole, and certainly the most dangerous of their foes, is telepathic Venusian worm, Mister Mind, who destroyed their hometown, brainwashed their friends, and murdered their cousin. Whenever Mind shows up, you can bet that the storyline will get darker, and Billy, Mary, and Freddy alike will take it very personally.
In the Golden Age comics, it was the Thinker, who appeared more often than any other villain. In the Silver Age, it was Gorilla Grodd, who was the one exception in his roster of Harmless Villain antagonists. In the Bronze Age it was Zoom/Reverse-Flash and his repeated attempts to outright steal his foe's life, who eventually killed his wife. Wally West in the Modern Age had Vandal Savage at first, and later the acclaimed Mark Waid run boosted Abra Kadabra to this role by making that villain much Darker and Edgier. Finally, Geoff Johns promoted Captain Cold to leader of the rogues — in the Silver Age it was usually the original Mirror Master or an outside villain in this role — and also contributed a new Zoom as a contender for the role, another villain who was far too dangerous to join the Rogues. And now that Barry's back, it seems to be the original Reverse-Flash again.
Another candidate for Wally's Arch Enemy under Waid is Mirror Master II; much was made of his role as a second-generation villain "reflecting" Wally; he discovered the Mirror Dimension at the same time as Wally began channeling the Speed Force, and he was a member of Luthor's "All Archenemies" Injustice Gang.
Then, the Justice League's arch-nemesis is the Legion of Doom/Injustice League/Injustice Gang.
The Justice Society's arch-enemy is the Injustice Society of the World.
Merlyn is considered Green Arrow's arch-enemy. Due to both being skilled archers on opposite sides of the law.
Existence, all superheroes, all living beings, and every single universe in the history, future, present moment, or wiped timeline of reality has The Anti-Monitor.
The Legion of Super-Heroes has three: Mordru, the Fatal Five, and the Legion of Super-Villains. The Fatal Five probably win the title for showing up the most often, but the L.S.V. has Lightning Lad's personal arch enemy Lightning Lord, and Mordru is certainly the most powerful of the three.
The Time Trapper is another arch-enemy of the Legion.
Spider-Man has various Arch Enemies. Part of the reason this situation arises is that the Green Goblin died in the 70s and spent a good 20-odd years dead before he came back to torment his foe, which is probably the record for dead A-list villains to beat; it also means that Ock and Venom are arguably more famous, even though the Goblin is easily the most dangerous of the three. The other reason is that the Goblin, as Norman Osborn, suffered frequent bouts of amnesia in the run up to his death so he didn't even remember that he was Spidey's arch-enemy, which helped Doc Ock who was the next most formidable villain. Venom appeared in the 80s and made his chops by being in some ways a more personal (and visually stunning) enemy than either of the other two (that and overexposure). So essentially, Spidey has three arch-enemies because they kept replacing each other. However, since his return the Goblin has cemented himself as Spidey's one true Arch-foe.
The Green Goblin. Unlike most superhero arch-villains, he actually is the most dangerous foe of his enemy, possessing far greater resources and deep personal information (he was the first to discover Spider-Man's secret identity) that the others mostly all lack (though one could argue that, apart from Osborn killing Gwen Stacy, Venom was originally more personal with his invasions of Peter Parker's life). There's also the whole "best friend's father" thing.
Doctor Octopus: What Peter could end up becoming if he abused his intelligence and powers. (Peter was even a former student of his in the animated series). Also the first villain to really defeat Spider-Man, completely shattering his confidence for a while, and is certainly the longest lasting and most recurring.
Venom: Evil Counterpart. Not only is he effectively an even stronger version of Spidey himself, but Peter's Spider-Sense doesn't work on him, which means Eddie / Venom could be right behind him without Peter knowing. Being bonded with the symbiote also gave Venom knowledge of Peter's secret identity, which Venom immediately used to scare Peter by harassing Mary Jane and Aunt May. Venom's initial grudge against him was kind of weak, but every adaptation makes it a lot more personal.
In addition to Spidey, Venom has Carnage, his son, as an arch-enemy. Spider-Man can't normally defeat Carnage on his own. The fact that Venom willingly comes to aid Spider-Man shows that he must hate Carnage more. Either that, or he just wants to be the one to deliver the killing blow.
The Brotherhood of Evil Mutants serves as a collective Arch Enemy to the X-Men as a whole, though they have generally been replaced with more and more frightening mutant supremacists such as Mr. Sinister's Marauders, the Hellfire Club, or the various henchman of Apocalypse.
A brave attempt was made to kill off Sabretooth and make new villain Romulus Wolverine's new arch-enemy, but it failed spectacularly.
Mystique could be considered Rogue's arch-nemesis. Due to Rogue feeling like she's being used. And what she did to Ms. Marvel led her to leave Mystique's Brotherhood.
For obvious reasons, Ms. Marvel can also be considered Mystique's Arch Enemy, in fact Ms. Marvel Vol. 2 #48-50 even refers to Mystique as Ms. Marvel's Arch Enemy.
Mystique also killed Ms. Marvel's then-lover towards the end of her first series. As for herself, Mystique may also consider the Shadow King her arch-enemy, seeing that he was responsible for her life-partner Destiny's death.
Cyclops and his family have Sinister, who is obsessed with gaining control of the Summers bloodline, and has repeatedly used cloning and various other gambits to get said control. Scott takes this very personally.
The Sentry's Arch Enemy is The Void, which is his own alternate personality. Complicated.
Ant-Man's is Ultron, the rogue robot he created. Though the villain he's most likely to face by himself is probably Whirlwind. Since Ultron's programming is based on Ant-Man's own thought patterns, this also means that Ant-Man is his own worst enemy. Used to be Egghead...but he died.
Iron Man's traditional Arch Enemy was The Mandarin, but he's faded a bit over time as the Yellow Peril aspect of the character is no longer kosher. Matt Fraction brought him back in big way during his run on Invincible Iron Man, however, nicely cementing The Mandarin's status as the worst that Iron Man's rogues gallery has to offer.
Seeing as thirteen different people have taken up the mantle, the Crimson Dynamo certainly is one of his most recurring and dangerous enemies, and has the best shot, after The Mandarin, of claiming this title. As a Communist holdout, the Dynamo also makes a useful counterpoint to Stark's capitalist ideology.
During the eighties and nineties, and up until his apparent death in the early 2000s, evil industrialist Justin Hammer served as the archenemy of Tony Stark. He was the mover and shaker behind "Demon in a Bottle", "Armour Wars I", and several other major arcs, and made repeated attempts to take down Stark Industries and their founder, all in order to increase his own profits. Hammer was one of the few villains Stark always took seriously, their hatred was definitely mutual, and in the end, his legacy lives on to this day in the form of his equally mad daughter and granddaughter.
The Punisher has Jigsaw. In The Punisher's case, "Arch Enemy" just means "enemy who's still alive". In the MAX imprint one could make a case for Barracuda for similar reasons.
Bullseye. A Psycho for Hire who typically acts as The Dragon to Kingpin, Bullseye's killed two of Matt Murdock's girlfriends, tried to kill his wife, Milla, and has generally dedicated himself to making Matt's life as hellish as possible; he's also inspired the likes of Lady Bullseye. In return, Matt wants Bullseye dead, and is willing to violate Thou Shalt Not Kill for him in a way he will for nobody else.
The Kingpin (who would also be an impressive fourth place on Spidey's Arch Enemy list, as well as a contender for The Punisher's). As the ultimate gang boss, everything that Daredevil fights against can be traced back to him, and he's orchestrated several collapses of Matt's life, during "Born Again", "Devil In Cell Block D" and various other arcs, hurting him worse than anyone else ever has. As practically the deuteragonist of the series, Kingpin will always be a part of Matt Murdock's life for better or worse, a fact that his late wife Vanessa, comments on in-series.
The ninja clan known as The Hand collectively fill the third slot on Matt's hit parade. They're among his most persistent enemies, many of his major foes (Elektra, Lady Bullseye, Kingpin) have either worked for them or tried to gain control of them at one point or another, they're the ultimate adversaries of his mentor, Stick, and worst of all, they want Matt to be their new leader. It's hard to get more personal than that.
Originally, as written by Stan Lee, it was the Owl. These days, he's reduced to second-string status; while still dangerous he just doesn't carry the emotional weight that Bullseye, Kingpin, and The Hand do.
Captain Mar-Vell had Thanos. Although Thanos did double duty as Adam Warlock's arch enemy, too. And he screwed with the Silver Surfer pretty seriously, too. After arcs like Infinity Gauntlet and other stories on that scale a case could be made that Thanos is the Arch Enemy of the Marvel Universe.
The Shredder to the Teenage Mutant Ninja Turtles Mirage and their Obi-Wan Master Splinter. Shredder goes down pretty early in the original comics. However the first issue clearly shows the backstory Splinter and Shredder have, that Splinter and the Turtles owe their origins to Shredder, and that Splinter trained the Turtles for the sole purpose of killing Shredder to avenge Hamato Yoshi. Regardless of how long Shredder was around for, he's still their archnemesis.
The Arch Enemy dynamic is played interestingly in the story. After Shredder was killed, the Turtles never really had another central enemy. A few issues show that the Turtles aren't really sure what to do with themselves with Shredder gone. In fact, in the City At War arc that capped off the original series, Leonardo argues that killing Shredder was more Splinter's goal than theirs.
Atomic Robo has the Nazi Baron Heinrich von Helsingard. Dr. Dinosaur may also qualify for Robo in modern times.
Thomas Edison for Nikola Tesla and, by extension, Robo.
One volume of Powers deconstructs the usual comic treatment of archenemies. It shows what were essentially the world's first superhero and supervillain. The two are immortal and have existed since humanity was still diverging from the ape, and have had a grudge just as long. When they meet for the last time in the present day, the hero, (who has a case of The Fog of Ages) demands to know why he and the villain have been fighting so long. The villain, whose memory is not impaired like the hero's, admits that he can no longer even remember what originally sparked their feud.
While Green LanternRebirth and Blackest Night initially pegged Parallax as the Arch Enemy of The Spectre, it seems that the Spectre's true nemesis is actually Butcher the Rage Entity. The Spectre exists to punish murderers, and Butcher is apparently the homicidal spawn of the first murder — the embodiment of murderous rage.
Sin City villains usually don't live past their initial story but Manute has menaced Dwight McCarthy enough times to count. Manute is dead now but he shows up anyway due to the nonlinear timeline.
The Yellow Bastard did go up against Hartigan a few times before kicking the bucket. We only ended up seeing two confrontations in the same story, though.
After becoming evil, being killed, and then brought back to life, Maxwell Lord has become the Arch Enemy to Booster Gold.
As with the Brotherhood being the collective Arch Enemy of the X-Men, The Avengers have the Masters of Evil.
Kang is also arguably the Avengers' Arch Enemy.
Baron Wolfgang von Strucker has served this mainly to Nick Fury, but also a bit to Captain America. Makes sense seeing as he's the leader of HYDRA.
The Fabulous Frog-Man is a Super Zero wearing the Power Armor of his father (Daredevil villain Leap Frog) which he cannot control so he just bounces around aimlessly and sometimes gets lucky. The White Rabbit is a ditzy Harmless Villainess that read too much Alice in Wonderland when she was a little girl and now dresses like a Playboy Bunny and pretends to be a Super Villainess despite having no powers or skills. They became each other’s arch-enemies because they are so pathetic nobody else would take them seriously.
The Martian Manhunter has had several contenders over the years including Commander Blanx and his expy (and J'onn's Evil Twin) Malefic. The best example, however, may well be Galactic Conqueror and walking engine of destruction, Despero. While Despero is usually a Justice League calibre threat, J'onn is always the one he attacks first, and he takes a perverse delight in forcing the Martian to telepathically relive the destruction of Mars. At one point, Despero went so far as to Mind Rape J'onn into believing he was on a Mars that hadn't been destroyed by Blanx and/or Malefic...only to then invade the dream and personally slaughter the psychic constructs of J'onn's family that he had created. J'onn hates Despero about as much as he hates anyone, and is usually the JLA member who ends up having to put the crazed being down at the end of his rampages.
In their fictional universe the characters from the two British ComicsThe Beano and The Dandy are arch enemies with frequent jokes but at the other's expense and infrequent raids between the comics. This arch enemy rivalry has died down quite alot since The Dandy's revamp. Also characters from within the two comics have their own arch enemies as well. Dennis the Menace (UK) has Walter the Softy, The Bash Street Kids had the Blob Street Kids, the Three Bears had Hank and Grizzly Gus (another more evil looking bear who hasnt been in the strip for years) and Desperate Dan had Dangerous Dan Mc Groo.
This arch-enemy comic rivalry was taken Up to Eleven in the Fleetway comic Whizzer and Chips which was one comic which was made up of two comics and these two comics and their characters were archenemies with even more frequent 'raids' in the two comics than with the Beano and Dandy
Darkhell had his own arch-enemy, Skroa (though more of a Rival than an actual one) before the Legendaries formed, but ended up defeating him.
Generation X (specifically M, although he targeted the rest of the team as well) had Emplate.
Moon Knight had Raoul Bushman, Marc Spector's commander in his mercenary days, who proved to be much more violent and ruthless.
More Marvel archfoes:
The Inhumans king Black Bolt's Arch Enemy is his insane brother, Maximus Boltagon the Mad. Currently (July 2012), the two have buried the hatchet, with Maximus loyally, if eccentrically, serving Black Bolt.
Havok used to have the Living Monolith, who fed off Havok's power.
Ex-mafioso hitman Underworld's Arch Enemy was his traitorous, sociopathic brother, Mr. Pain, whom he killed.
The Johnny Blaze/Zarathos incarnation of Ghost Rider's Arch Enemy is Mephisto.
The Danny Ketch/Noble Kale incarnation of Ghost Rider's Arch Enemy is Blackheart.
Shi'ar empress Lilandra Neramani and her sister Deathbird.
Mickey Mouse as seen in more recent comics has his own kind of dynamic with his two arch enemies Pete and the Phantom Blot. Mickey is typically more or less an Amateur Sleuth, naturally opposed to both of them as professional criminals. Pete is generally shown as a more crude but very experienced and enterprising criminal, whereas the Blot is a shadowy criminal mastermind. Pete is not completely evil and has been shown with a kind of affection towards Mickey as an opponent and is more prone to end up in an Enemy Mine situation with him, whereas the Blot is closer to being simply sociopathic. The two can even get contrasted in the same story, with Pete more human and the Blot more effortlessly smooth and evil. It's still Depending on the Writer.
Matt Fraction's Hawkeye ongoing is seemingly setting up Madame Masque as Kate Bishop's arch-enemy. While it's for largely petty reasons (Kate tied her up and stole her identity for an issue), Masque has devoted an absurd amount fo time to wrecking Kate's life ever since.
Spider-Woman and Madame Hydra/Viper, due to Jessica being raised by Hydra and possibly becoming the next Madame Hydra.
From the New X-Men, Elixir and Wither. Both were in a love triangle with Wallflower before she died, and have the opposite powers to one another. Elixer heals, Whither... whithers things.
Magik and Belasco. Belasco turned Magik into what she is, and she has never stopped blaming him for this, and usurped him as ruler of Limbo. Eventually, Belasco's daughter took over this role for Magik.
Judge Dredd and Judge Death. The former is a trigger-happy fascist enforcer of a post-nuclear future, the latter a psychopathic undead monster from another dimension who wants to slaughter every living thing.
Nero: In the early stories this role went to Matsuoka, a Fu Manchu like antagonist. Later Ricardo the Napolitan maffiosi became Nero's most frequent target.
Astérix: Julius Caesar would be this, even though there's a mutual respect between the Gauls and Caesar and they usually leave each other alone. Caesar is often seen as a Voice Of Reason and above the corruption of many of his legionnairies. He will defend the Gauls if he understands that some Romans have done them wrong in a way that even he couldn't defend.
Jommeke: Jommeke and his friends are often confronted by Anatool, the servant nobody can trust. However, he is somewhat of a Harmless Villain, seeing that Jommeke and his friends can easily thwart his evil schemes. De Koningin van Onderland ("The Queen of Onderland") on the other hand doesn't appear that much in Jommeke's stories, but when she does she is generally considered to be his most frightening and dangerous opponent.
Lucky Luke: Lucky Luke often faces off against the Daltons.
De Kiekeboes: Balthazar is the most recurring antagonist in the series, though generally considered to be a Harmless Villain. Far more dangerous are Timothea Triangl- a Bond Villain who underwent a sex change- and Dédé La Canaille, a criminal who wants to murder Kiekeboe for putting him into jail.
The Smurfs: Gargamel who, in the comics at least, wants to turn the Smurfs into gold. In the animated series he simply wants to eat them.
Tom Poes: Bul Super and Hiep Hieper. Even though Joachim Sickbock and Hocus P. Pas are far more dangerous.
Donald Duck: Scrooge McDuck often combats the Beagle Boys. His business rival Flintheart Glimgold sometimes funcions as his own personal arch enemy too. However his most dangerous opponent is Magica Despell, who threatens to steal his lucky dime and melt it into the Vesuvius volcano.
Similarly Donald Duck considers both Gladstone Gander and Neigbour Jones his personal arch enemies.
Urbanus: Urbanus often fights off against Jef Patat, a sleazy trickster.
Catwoman had Black Mask (the original version) as her arch-enemy in her early-2000s series. In a Darker and Edgier twist, she ended up murdering him after he tried to fridge her friends and relatives once too often.