Nicholas Pike became this to the Flash after he murdered Barry's brother Jay.
Oliver Queen, through his many disguises, has earned the mutual ire of many dangerous foes, but the biggest in his Rogues Gallery are:
Malcolm Merlyn, Oliver's first personal enemy, and the one who was most similar to him as an Evil Counterpart as a man who lost himself to the darkness; its a small wonder why Merlyn calls himself the "Dark Archer". Being responsible for sinking the Queen's Gambit, and leaving Oliver stranded on Lian Yu for years, Malcolm plays a huge role in ruining Oliver's life and setting him on the path of becoming the vigilante he is today. In their rivalry, Merlyn has been responsible for the deaths of three important people in Oliver's life, and manipulating Thea against Oliver multiple times. Even after he and Oliver came to an Enemy Mine against Ra's al Ghul, Merlyn ended up betraying Oliver to H.I.V.E. after he gets humiliated from being beaten in a League challenge, resulting in Oliver cutting off Merlyn's hand and stripping him of the title of Ra's al Ghul. Things are so personal that, during said duel, Malcolm makes it clear that the only way their feud will end is when one of them is dead. Merlyn would ultimately perish on Lian Yu performing a Heroic Sacrifice for Thea. To add fuel to the fire, every time Oliver is required to think of an arch foe, Merlyn is always first on the list.
Oliver's adversial relationship with Malcolm is further complicated by the paternal slant added to it. Malcolm was the father of Oliver's best friend Tommy (and, as he later learned, his sister Thea), and prior to the death of Rebecca, acted like a favorite uncle or even a second father to him. Even after Malcolm grew cold, he still had some fatherly affection for Oliver, regarding him as a Like a Son to Me, and deeply regretted his "death". Ultimately, part of their animosity is driven by this facet of their relationship. In Malcolm, Oliver sees all the qualities he hates about himself, and it's implied Malcolm is partially resentful of the fact that, out of all three of the Queen/Merlyn progeny, the one most similar to him and also has the most potential is the one that does not share so much as an ounce of his blood.
Slade Wilson, a.k.a Deathstroke, who served as a much more personal enemy, with the most crushing blow being when he killed Oliver's mother in front of his eyes. At first friends, Slade was set on a never-ending vendetta to ruin Oliver's life after being injected with the Mirakuru serum, since the serum causes him to blame Oliver for causing Shado's death. However, Oliver has more-or-less accepted the fact that what happened with Slade was partially his fault for not telling him the truth about Shado's death when he had the chance, and is happy to leave Slade imprisoned instead of killing him due to that and their formerly close relationship. This decision leads to Slade working the Mirakuru out of his system, feeling remorse for his actions against Oliver and forming an alliance with him against Adrain Chase that reignites their old comradery.
It's also worth noting that Oliver and Slade are also part of a line of "Deathstrokes" and archers that share an animosity. Before them, it was Yao Fei and Billy Wintergreen, and after them it could be Connor Hawke and Grant Wilson in a possible future.
To avenge his father's death at Oliver's hand, Adrian Chase, as Prometheus, terrorizes Star City and kills several innocent people, recruits people into turning against Oliver, manipulates Oliver into killing Felicity's boyfriend, psychologically tortures him to the breaking point, and eventually forces Oliver to turn the city against his superhero identity, branding Green Arrow a criminal. Meanwhile, under the guise of a False Friend, Chase butters him up to gain his trust, aiding him as one of his closest confidants within his administration and even helping Diggle get out of military prison. Once the charade is broken, the two don't even try to hide how much they hate each other, making it very clear that their war will only end when one of them is dead. In fact, Oliver is even willing to ask for help from Malcolm and Slade, as he's that desperate to beat Chase.
Malcolm Merlyn is also high on many people's hit list, but is chiefly a menace to:
Moira Queen, who he had a brief affair with after the death of Rebecca, resulting in Thea. Years later, he sabotaged the Gambit, resulting in her husband Robert's death, and then coerced her into the Undertaking by threatening to do the same to Thea and her new husband Walter. She eventually betrayed him the night his ambitions were to take fruition at the behest of Oliver, and when he tried to force her into telling Thea that he was her father, she told Ra's al Ghul (who was not happy with Malcolm after the Undertaking) that he was still alive, making her the indirect cause of every misfortune that has befallen him post-Season One.
Nyssa, who dedicated her life to bringing Malcolm down after he killed Sara. When Malcolm becomes Ra's al Ghul, Nyssa did everything in her power to overthrow him, even destroying the Lazarus Pit to spite him. Eventually, Malcolm came to hate Nyssa too, willing to betray a truce between them when she had offered a cure for his daughter's life. In the "Doomworld" altered reality, the only thing Malcolm used the Spear of Destiny to do that did not benefit whatsoever was to banish Nyssa to a miserable, closeted life in Ohio.
Even his own daughter, Thea, who he brainwashed into killing Sara Lance in his gambit to end his debt to Ra's al Ghul, which also deepened Nyssa's hated for Merlyn, has it out for him. Thanks to his refusal to give up leadership of the League for her and handing Oliver's son William over to Damien Darhk, she appears to have rejected him and he appears to have gone full-blown villain. They do face off in combat, but he won't kill her.
Floyd Lawton, a.k.a Deadshot, was this to John Diggle for killing his brother, Andy. However, His Noble Demon tendencies later endeared him to Diggle and they eventually came to an understanding that leads Lawton to sacrifice his life to get Diggle home to his family. Ironically, Andy would become Diggle's foe after it was revealed he faked his death to join H.I.V.E., until, more ironically, Diggle himself would end up killing Andy.
Detective Quentin Lance had Barton Mathis, the Dollmaker.
Damien Darhk is this to all of the Original Team Arrow for, amongst over crimes, threating Laurel to get Quentin to join H.I.V.E., ruining Oliver's mayoral campaign, crippling Felicity and leaving her paraplegic, kidnapping Oliver's illegitimate son William, and turning Diggle's brother against him. After he kills Laurel purely out of spite, it doesn't take long for all of Team Arrow to bitterly hate him and want him dead above all else.
Darhk was also Ra's al Ghul's nemesis, having been his friend before they became rivals for the title of "The Demon's Head". While they havn't interacted in the proper sense, Ra's entire plan to destroy Star City was not only to ensure Oliver's ascension as his heir, but to kill Darhk as well.
Next to her father, Thea's biggest enemy is Lonnie Machin, a.k.a Anarky.
Felicity Smoak dubbed the Bug-Eyed Bandit, Brie Larvan, as her nemesis after she gives her a run for her money in hacking. She also had a rocky relationship with her father, Noah Kuttler a.k.a the Calculator, before his HeelFace Turn.
Dinah Drake had Sean Sonus, for killing her cop partner and lover. She spent three years hunting him on a Roaring Rampage of Revenge, until she killed him, only to quickly gain another nemesis in the form of Laurel Lance's Earth-2 counterpart, Black Siren, ironically for the same reason as Sonus, until the two were able to bury the hatchet to honour of Quentin Lance.
Due to his machinations to create a criminal empire for himself, Ricardo Diaz quickly became the arch foe for Team Arrow as a whole, especially after he orchestrated events to get Oliver in jail, caused the team to briefly fracture from mistrust and poor communication, murdered Quentin Lance, and forced Oliver into the position of ousting his secret identity and surrendering to the FBI's custody. After he personally attempts to murder her and William to hurt Oliver, Felicity in particular grows to utterly despise Diaz, to the point that she tries to kill him while he was in police custody.
The Flash (2014)
Barry has almost as many as Oliver. Ironically, despite being the nicer and arguably more compassionate of the two, a strong argument could be made that Barry hates his arch-enemies more than any other lead in the Arrowverse hates theirs.
Eobard Thawne, a.k.a the Man in the Yellow Suit a.k.a the Reverse-Flash. Thawne murdered Barry's mom, framed his dad for it, and then manipulated Barry's life under the guise of "Dr. Harrison Wells". He is Barry's most personal enemy, and their destinies are so intertwined that one cannot exist without the other, thus they will never be fully rid of one another — a fact that only makes them hate each other more. Even when talking about his other hated enemies with Nora, Barry makes it clear to her that Thawne is the one he hates the most, especially after Thawne manipulated Barry's future daughter, Nora, into to save himself from his execution at Iron Heights in 2049, resulting in Nora being Ret Goned.
Leonard Snart, a.k.a Captain Cold, was identified as the Flash's "nemesis" by Thawne. He was certainly a persistent and dangerous foe, being the first to utterly defeat Barry, then torturing Cisco to learn the Flash's identity, to finally tricking Barry into an alliance just so he could betray him. However, their animosity declined after Barry saved Snart's sister from their abusive father, and, after Snart ended up pulling a Heroic Sacrifice for the Legends, he and Barry become straight up become Friendly Enemies when Barry time travels to before his death to ally with him.
Earth-2's Hunter Zolomon, a.k.a Zoom, who pulled the same trick as Thawne did by impersonating "Jay Garrick" (the Earth-3 counterpart to Barry's father, no less) and presenting himself as an ally all so he could steal Barry's speed to cure himself of Velocity poisoning. As Zoom, he beat the crap out of Barry several times, once breaking his back and humiliating him in front of all of Central City. Then there's what he did to the rest of Team Flash: he kidnapped Jesse Wells to blackmail Harry into helping him and betraying the rest of the team, kidnapped Wally to force Barry to give up his speed, and then kidnapped Caitlin to invoke Stockholm Syndrome on her, traumatizing her and leaving her with PTSD. And, for the final finishing touch, he murdered Henry Allen in the very same spot where Eobard Thawne murdered Nora Allen, right in front of Barry's eyes. After that, Barry wants him deader than dead and looked very ready to do the deed, inspiring a deep hatred in him that not even Thawne was capable of. While Barry ultimately didn't kill him (though he was very close to doing so), he did engineer the events that led to the time wraiths subjecting Zolomon to a Fate Worse than Death.
After Snart leaves with Rip Hunter, Grodd takes his place as Barry's top non-speedster enemy, being a constant thorn in the Scarlet Speedster's side and his most dangerous non-Arc Villain enemy. By the time "Attack on Gorilla City" happens, Grodd has forgone all former attachments and his sole concern is getting revenge on Barry for exiling him to Earth-2 by any means necessary. Barry even contemplates killing Grodd to end his evolving threat, which Grodd even encourages him to do, seeing it as the only way to "end it".
Clifford De Voe, a.k.a the Thinker, who was remembered as being among the Flash's biggest enemies by Abra Kadabra and the Reverse-Flash. In his quest to begin the Enlightenment, the Thinker subjected the Flash to defeat after defeat with his superior planning and intelligence, with the biggest blow being when he framed Barry for murdering him, ruining his reputation as a CSI and sending him to Iron Heights Prison. Once it seems that he appears to kill the Elongated Man after successfully killing all the other meta-humans he promised to protect, Barry comes to regard De Voe with a loathing that rivals that of his with Zoom and Thawne.
Joe West had the Mardon brothers. Clyde killed Joe's partner, and Joe eventually killed Clyde in defense of Barry. Unfortunately, Mark Mardon did not take the death of his little brother well, and goes gunning for Joe until Barry alters the timeline and Mark's vendetta goes unresolved.
Aside from the hatred for Eobard Thawne he shares with Barry, Cisco Ramon originally had Hartley Rathaway, a.k.a the Pied Piper, but after Barry alters the events of The Sound and the Fury, Hartley undergoes a HeelFace Turn and becomes an ally.
General Wade Eiling was the arch-enemy of Firestorm, but only the Martin Stein/Ronnie Raymond fusion. After the Reverse-Flash hands Eiling over to Grodd, Eiling turns his resources towards stopping Grodd instead of further hunting Firestorm.
In the "Flashpoint" timeline, Wally West had Edward Clariss, a.k.a the Rival, for an arch foe. However, in the main timeline, he has yet to develop a personal animosity with an adversary.
Savitar is this to Team Flash as a whole, having found a way to irk off every one of them. Case in point, in a possible future, after he murders Iris, Savitar cripples Wally both physically and mentally, corrupts Caitlin beyond recovery, and more-or-less breaks Team Flash until Present!Barry gets them back together. This is taken even further once it's revealed that Savitar is a time remnant of Barry who turned evil.
Abra Kadabra is this to Gypsy for killing her former lover among many other people. He also implies that he will one day become one for the Flash.
John Constantine has several both from his own show and with his time with the Legends:
The demon Nergal, for killing Astra and taking her soul to Hell in an exorcism gone wrong; not helped by the fact John was the one who summoned Nergal in the first place. He's made it his mission to go to Hell to save Astra and then go after Nergal. Astra being corrupted but a damper on those plans though.
Papa Midnite, a Voo-Doo crime king and John's primary nemesis and Evil Counterpart in magic, though he's something more akin to The Rival instead.
The demon Neron, for taking his lover Desmond to Hell and tormenting him about it and then spending "Legends" Season 4 going after the Legends just to twist the knife in further.
Mari McCabe had her sister, Kuasa, and then Benatu Eshu.
Kara Danvers has many enemies, but by virtue of being an All-Loving Hero, she doesn't have the kind of personal hatred for her worst ones that Oliver and Barry have for theirs. However, she openly calls Leslie Willis, a.k.a Livewire, her nemesis, with Winn commenting that even mentioning Livewire's name causes Kara to get defensive. Ironically, Livewire would end up performing a Heroic Sacrifice to protect Kara from Reign.
Maxwell Lord was also a recurring menace to Supergirl in her early career, but hostilities between them decreased as time went by.
Also, even tough they have only faced each other once so far, Rick Malverne is Supergirl's only enemy to truly get under her skin by kidnapping Alex and threating her life to make Supergirl his pawn, with her unable to find a way to counter his various contingencies.
J'onn J'onzz views the entire White Martian race as this for their part in his kinds extinction, but he begins to lighten up to them after meeting M'gann M'orzz.
Though both quarrels are entirely off-screen, both Lex Luthor and General Zod are recognized as arch foes of Superman by the public of Earth-38.
CADMUS as a whole serves as this to the Department of Extra-Normal Operations, with Lillian Luthor being a big target for Alex Danvers due to her forcing Alex's father to work for CADMUS.
Lena Luthor has Morgan Edge. After Lena outbid him for Cat Co, Edge swore to crush her as a business rival. After multiple attempts to frame her for crime, and even an attempted murder, the feeling is more than mutual between them.
Lena also has her own brother, Lex Luthor. Lex was manipulating Lena's research from the start and when he needed her to speed the process he has her boyfriend shot. He also leaves a note explaining it was all personal and he uses the notes he wrote of all of Lena's failures and shortcomings as a kid to taunt her.
In addition to J'onn, Manchester Black is the nemesis of Ben Lockwood (aka Agent Liberty) since he was the one that murdered Black's fiancee Fiona.
DC's Legends of Tomorrow
Vandal Savage is this to Hawkman, Hawkgirl, and Rip Hunter. He's been murdering the former two's various incarnations for thousands of years to maintain his immortality, and murdered the latter's wife and young son just for opposing him, and to spite Rip after he lets slip that that is why he is hunting Savage throughout history.
Damien Darhk becomes this to the Legends once they start identifying themselves as such. After a brief run in with him during their time with Rip Hunter, Darhk gets recruited into Eobard Thawne's Legion of Doom to oppose the Legends until he is returned to his place in time, and is later resurrected from his death in Arrow to serve as a representative for the Cult of Mallus. Of the Legends, Darhk has the biggest animosity with their leader, Sara Lance, due to him murdering her sister in 2016. Ironically, after seeing what Mallus plans for his daughter, Nora, Darhk joins forces with the Legends, even getting friendly with a few of them, and ultimately dies protecting his daughter.
Darhk's colleagues in the Legion of Doom also serve as this to the Legends, with Vixen having her sights set on the Reverse-Flash for killing Hourman, while Thawne thinks himself a Foil to the Atom, Captain Cold trying to persuade Heat Wave back into a life of crime, and White Canary becoming the Dark Archer's main target after he reveals his part in crashing the Queen's Gambit to her.
Jonah Hex has Quentin Turnbull.
Neron. At first he was just after John Constantine and targeting the Legends just to mess with him. But after killing Hank Heywood and then possessing Ray Palmer, the rest of the Legends grew to want him gone as well.