The 1950s incarnation of Captain America ("Commie Smasher") was (through the magic of Retcon) explained away as an obsessed fan of the original who insisted on replacing him during the time when he was presumed dead; while the US government decided to humor him, the faulty version of the Super Soldier enhancement process eventually drove him insane. While he was eventually captured and placed in suspended animation, he broke out years later and attacked who he thought was another Captain America imposter - the real Captain America, who had defrosted from his own accidental suspended animation.
There was also Protocide, a test subject for the Super Soldier serum who went crazy with pain, got put in storage for many years, then was let out by AIM and manipulated into going after Steve Rogers. There was some 'opposite' motifs going on in his appearance: his costume was red instead of blue, and he had a far pointier shield.
Black Adam was the Evil Counterpart of Captain Marvel, his predecessor as a bearer of the power of Shazam who became corrupted by its power.
Similarly, not only was the Green Lantern foe Sinestro once a Green Lantern himself, in Post-Crisis continuity he actually trained Hal Jordan in the use of his powers before becoming his nemesis.
In more recent times, there are even more popping up, but not all evil (so sort of non-evil counterparts to the evil counterparts): while the green represents will, and yellow represents fear, there's now violet (love), blue (hope), red (rage), orange (greed), and indigo (compassion). And eventually black (death), which is the really evil counterpart.
Kyle Rayner got 2 energy-wielding/manipulating Evil Counterparts, himself. On the 'ring-wielder' side of things, Alex Nero - who was Ax-Crazy, and possibly killed his parents as a teenager. On the 'might've become' side of things, Effigy, who was what Kyle might've been if he hadn't matured and gained a sense of responsibility about the ring and super-heroics in general.
Some individual members of the Sinestro Corps are evil counterparts of specific GLs; for instance Arkillo (Evil Kiliwog) and Ranxx the Sentient City (Evil Mogo the Living Planet).
The criminal Killer Moth originally patterned himself as an Evil Counterpart to Batman... but quickly sank to a third-string position in the Rogues Gallery. As we said, the Counterpart is sometimes a Big Bad, but not always. It was probably a bad idea to name himself after something bats eat.
Continuing in that vein, the Wrath was a Pre Crisis villain who was even more of a Batman counterpart, down to duplicating much of his origin (his parents being killed in a shootout by Commissioner Gordon in his days as a rookie beat cop). Not only did he not become a Big Bad, he was essentially a one-shot opponent.
And both Prometheus and the Wrath are at large once again. Yes, they're practically the same person except for Prometheus' focus on technological gadgetry.
Bane was created as something of an Evil Counterpart to Batman, having trained his mind and body while in prison (serving part of his late father's term). The big difference is Bane's use of the chemical Venom to give himself Super Strength. Bane could also be considered an evil counterpart to Doc Savage, particularly with regard to his original aides.
Two-Face also mirrors Batman in his dual nature - Batman's identities are secret and united in their goals while Two-Face's are obvious and opposed. Harvey Dent started out with the exact same goal as Bruce, making him an example of what Batman could become if he loses his self-control, and was a close friend and confidant of either Bruce or Batman in most continuities.
While Bruce Wayne had caring, loving parents, Tommy Elliot's were both cut from the Rich Bitch cloth (and his father was an abusive alcoholic). To keep himself from harm and create a better life for himself, he arranged a car accident that killed his father and left his mother an overbearing cripple. Tommy hated that Bruce's dad saved his mom and that Bruce eventually got the life Tommy wanted for himself. Upon being told by the Riddler that Bruce was Batman, Tommy became Hush, an archetype of Batman who is a criminal mastermind.
Owlman and Talon, Batman and Robin's counterparts from Earth-3, the Evil Counterpart Universe.
The Ax-Crazy Black Mask. Like Bruce, he was the son of wealthy parents who died due to unnatural causes. The difference is that Black Mask happened to kill his own parents and run his company into the ground with his own incompetence, before becoming a masked and increasingly violent crime lord. He even met Bruce as a child. He's as much of an Anti-Bruce Wayne as an Anti-Batman.
Catman was going to be one of these for about 5 minutes. Add in the Red Hood (formerly Jason Todd, the 2nd Robin, a vigilante who kills villains left and right when he isn't in Countdown) and Batzarro, which, yes, is a thing that really exists, and he has about a dozen of these.
Deadshot is still another example, the son of a wealthy Gotham family, a Rich Idiot with No Day Job by day and a Bad Ass Normal by night. The primary differences in his life from Bruce's are that he attempted to stop the tragedy as it happened, but his Abusive Parents survived while Deadshot accidentally killed his beloved brother. Already The Unfavorite with both parents, Deadshot initially took to vigilantism and crime out of boredom, before graduating to both Blood Knight and Death Seeker. Batman, in contrast, began his career out of a compulsion to serve justice and later developed a stronger desire to ensure that Everybody Lives.
Batman's gallery is built on the Evil Counterpart concept, mainly because writers acknowledge that what Bruce does isn't exactly sane and love to point out how easily it could have gone another way.
To the point where its hard to find a villain who isn't an evil counterpart of some facet of Batman. The Joker himself has pointed out they are both the results of something traumatic and life shattering (maybe), but to add, the Scarecrow uses fear just as much as Batman does, the Riddler uses his intellect more effectively than physical strength, Ra's Al Ghul is a man with a lifelong war on crime, and Mr. Freeze is motivated into his actions by the person he loves most in the world.
In Death Of The Family, while The Joker has always been this to Batman, this time he is figuratively borrowing pages from Batman's book, like turning off the lights to get the drop on a group of his enemies, and finding out the Batfamily's secrets so he can hit his enemies where it hurts!
Dr. Hurt is Thomas, and to a lesser extent, Bruce Wayne's evil counterpart, using his wealth and influence for evil.
James Gordon Jr. was described by Scott Snyder as the exact opposite of everything his father stood for.
Venom is Spider-Man's Evil Counterpart, created when he symbolically cast off the darkness within him. Later, when Venom became an Anti-Hero, Carnage was created to be his Evil Counterpart. Years later, Eddie Brock became Anti-Venom and was the Good Counterpart to the third Venom.
Toxin is Venom's Good Counterpart.
The tables have been turned on that one, Eddie Brock is now Toxin, and now Flash Thompson, the current Venom, is Eddie's Good Counterpart.
Spider-Man has had several villains meant to be his thematic opposite, from the Fly (who gained his powers in an accident much like Peter's own, but never stopped "looking out for number one" and blamed everyone else for his shortcomings) to the Scorpion (ditto; Bonus points for being an arachnid, too. And then the original Scorpion became Venom for a while). Dr. Octopus shares many personality traits with Spider-Man and is even based on another 8-legged creature. Less obviously, there's the Spider-Wasp.
And The Thousand, an old schoolmate of Peter's who witnessed the accident that turned him into Spider-Man. He went back to the lab after hours, found the dead spider, and ate it. It turned him into a being capable of becoming a living swarm of spiders. He ended a promising criminal career as a single very ambitious spider who failed to notice a large human foot coming down behind him...and—squash.
Joe Straczynski's run has Ezekiel, through not that evil — he is quite good-intentioned but lacks Peter's heroic qualities (through Peter inspires him to some acts of heroism at one point or two). They have the same powers, but while Peter got his by accident, Ezekiel actively sought them because he couldn't live with feeling powerless. While Peter sacrifices his well-being to help people as superhero, Ezekiel uses his powers for personal gain. While Peter never let anything gets in his way of helping people, Ezekiel always hides behind excuses, when he could be a hero. When having to suffer consequences of their respective actions, Peter accepts them while Ezekiel tries to trick him into taking his place. In the end Ezekiel has a Heel Realisation and makes a Heroic Sacrifice to save Peter after their minds merged for a moment and an exchange of memories occured.
Another one from the same run is Charlie Weiderman — he was a nerd picked upon through high-school just like Peter, but grew up harboring grudges, while Peter not only forgave but befriended his high-school bully, Flash Thompson. When Charlie gets powers, by accident, he immediately goes to exact revenge on anybody who wronged him.
Sabretooth is portrayed as Wolverine's evil similar, with near identical powers and completely feral. And he's implied to be Wolverine's half-brother; if he is, then they've hated each other their entire lives. Interestingly however, both characters were introduced separately from each other, Wolverine first appeared (with slightly different powers than his X-Men debut) in the Hulk comic, while Sabretooth was introduced (with no powers at all and claws that were only part of his gloves) in the pages of Iron Fist.
This may not be quite so coincidental, as Chris Claremont and John Byrne were working on the Iron Fist title around the same time as their classic run on X-Men.
Wolverine's enemy Silver Samurai has an inversion of this with Ebon Samurai. Word of God states that Ebon Samurai was a police officer that was killed by Silver Samurai, only to be resurrected as a vengeance-driven superhero.
Following in their dad's footsteps, X-23 and Daken seem to be heading towards this type of relationship with X-23 being the "good" counterpart and Daken being the "evil" counterpart.
Flintheart Glomgold, of the Disney Ducks Comic Universe (and later DuckTales) is an evil counterpart to Scrooge McDuck - every bit as ambitious as Scrooge, almost as wealthy, but with none of Scrooge's redeeming factors, such as his honesty and sense of fair play.
DuckTales even increased the similarities by making Flintheart Scottish, the same nationality as Scrooge - though this was because he was originally South African in the comics, and they wanted to avoid unfortunate connections.
The Marvel Comics series Sleepwalker has an Evil Counterpart in Psyko, who possesses warping abilities similar to Sleepwalker's. Sleepwalker, an alien devoted to protecting the minds of innocent people from insanity, became fused with the human Rick Sheridan when he found himself trapped in Rick's mind, whereas Psyko was created when a human Serial Killer became fused with a demonic creature from the Mindscape, giving him the ability to spread his madness like a disease, Mind Raping everyone around him.
Other than their common teacher, however, the two men actually do not have very much in common, their life histories and backgrounds are very different. Doctor Strange did not even realize the supernatural was real until his middle years, and only began to pursue it because an accident crippled his surgical abilities, his background is actually scientific. Mordo was raised supernatural, from a supernatural family, and steeped in evil from early youth, his background is more traditionally magical/occultist, and he always sought power.
The Catwoman series tried giving Selina an Evil Counterpart a couple of times. One was She-Cat (another cat-based thief, but a less skilled and less ethical one, who eventually turned out to know Selina from when they were in the same orphanage) and another was Hellhound (a male chauvinist who'd been trained by the same Old Master, and been The Unfavorite). Neither of them caught on.
Aquaman has had several evil counterparts. The most obvious is the Ocean Master, his own brother. Others include Charybdis, Evil Twin Thanatos, and the Thirst.
In Circle of Blood, the first Punisher miniseries, Castle fights against a brainwashed army of criminals, all patterned after him.
Judge Dredd has the Dark Judges, who have taken the policing style of the Judges to an extreme where Mega-City One is practcally Utopian.
The Mandarin is more the anti-Stark than the anti-Iron Man. Stark is a thrill-seeker. Mandarin participates in gladiatorial games so he can thrill to putting his fist through someone's head. Stark sacrificed his health so he could help the world. The Mandarin sacrifices everything and everyone around him to become stronger.
The various Crimson Dynamos and Titanium Men were originally created to be Communist (and therefore, at the time) Evil Counterparts to Iron Man. Since The Great Politics Mess-Up, they tend to get played more as the rival or even the Worthy Opponent.
Justin Hammer is the anti-Stark-as-businessman. While Tony uses his money to fight crime, Hammer uses his to sponsor it.
The Hulk now has the Red Hulk. The Leader and the Abomination probably fit this role too.
Oddly enough, Hulk's Rogues Gallery also includes someone else's Evil Counterparts. The U-Foes are a group of four villains whose origin, powers, and personalities are all extremely similar to those of the Fantastic Four. Strangely, they have never faced the FF despite all of the characters being Marvel Comics characters.
Titania too. Like Jennifer, she was also a shy wallflower in high school that gained superpowers later in life. There are a few key differences though. She-Hulk never asked for her powers (she adjusted well enough though) while Titania was so desperate to be powerful and special that she let Doctor Doom experiment on her. She-Hulk's transformation helped her gain real confidence both as She-Hulk and as Jennifer Walters. Titania's powers act as a crutch and deep down she is still the insecure Mary MacPherran. Titania resents She-Hulk specifically because She-Hulk is stronger than her in every way.
"Except for an accident of circumstance, I could have been your Luke Skywalker, and he could have been me. After all, we were both farmboys who loved to fly." Baron Soontir Fel, the best non-Vader pilot in the Empire, says this to Wedge Antilles after he's captured by Rogue Squadron. Farm Boy origins aside, he's actually closer to being the counterpart to Wedge, who also happens to be his brother-in-law. Fel is distinctly not evil; he's Imperial, which does put him on the "wrong" side, but he's not an evil man. He actually joins Rogue Squadron for a time, before disappearing and ending up as part of the Empire of the Hand.
Moon Knight had Evil Counterpart villains for his Marc Spector identity (Bushman), his Steven Grant identity (Midnight Man), and his Moon Knight persona (Black Spectre).
Starman's Jack Knight and Nash were on their respective sides of the law mainly because their fathers pushed them there.
All four Flashes have fought a "reverse flash" of some sort or another. Jay Garrick had the Rival, an old college professor who discovered his power source and committed crimes dressed like the Flash. Barry Allen fought Professor Zoom, a stalker who wanted to destroy everything Flash loved. Wally West's counterpart is Zoom, a former profiler who is convinced that super heroes are only effective if they lose people they care about. Bart Allen had Inertia, an evil clone of himself.
Barry Allen also fought his prior to unknown twin Malcolm Thawne aka Colbalt Blue who established his own legacy of evil that mirrored the Flash Family. Including Professor Zoom.
From the Knights of the Old Republic comics, both Big Bad Haazen and hero Zayne Carrick are relatively weak Force-sensitives who were considered failed Jedi apprentices. The difference is that Haazen allowed his bitterness and jealousy of his more talented peers to utterly consume his life, while Zayne still maintains his fundamental human decency no matter what. The series' other main protagonist, Jarael, now has one of her own in the form of Chantique, who represents what Jarael would be if she allowed herself to be dominated by her Dark and Troubled Past.
Raven Red in the Jet Dream feature. Like Jet, she's also a top-notch aviatrix with an all-girl team.
Reed Richards and Doctor Doom: archenemies, both intellectually-inclined supergeniuses, both master inventors, both with major strengths in technology, both hammy and prone to Sesquipedalian Loquaciousness, both pretty similar in personality once you factor out Doom's This Is Your Brain on Evil. A lot of their battles consist of them passive-aggressively complimenting each other's moves in ways that often sound a lot like two computer geeks playing together. The key difference between them usually centres on how they handle responsibility; Doom's entire motivation stems from the fact that he can't accept that it was his own error, not Reed's interference, that caused the accident which scarred him, and maintains his vendetta to avoid having to acknowledge that he was at fault all along and Reed is just a little bit smarter than him, while Reed is a lot more willing to accept fault when he's in the wrong and will attempt to make amends or correct his mistakes.
Doom is sometimes also used as an Evil Counterpart to Iron Man: both battlesuit wearing geniuses with serious character flaws.
The All-Purpose Power Tool itself has an Evil Counterpart in Ironarm's Worldbeater, a massive, polluting contraption with bolted-on components that tears up the landscape as it works.
Death Mayhew, commander of the Nazi flying group the White Lions, was this to Blackhawk.
While they never met, Kevin and Miho from Sin City were meant to be counterparts of one another. They're both improbably strong and neither ever speaks. Kevin is obviously the evil one while Miho is at least the Anti-Hero version.
Marv and Manute from the same series also fit as they are both big, scary determinators. Dwight all but lampshaded this when he brought Marv in to deal with Manute. Bonus points are given to the fact that while Manute is evil, well dressed, and highly educated, Marv is good (in comparison), a bit of a bum, and not very book smart.
Gideon Graves to Scott Pilgrim. They are both assholes who gloss over their misdeeds with Self-Serving Memory, and are horrible to their girlfriends. Gideon takes his Yandere tendencies Up to Eleven, while Scott eventually realizes his faults and genuinely wants to change and be a better person.
Nancy Thompson has become Freddy Krueger's good counterpart in Nightmares on Elm Street, as she has developed dream powers of her own that she uses to help people. Unfortunately, she hasn't fully accustomed to the dream world and lacks the years of experience that Freddy has.
The Beano has Pa Bear and Grizzly Gus two bears who love food in a strip called The Three Bears. The Dandy's most iconic strip Desperate Dan has Dangerous Dan Mc Groo who looks almost exactly like Desperate Dan, albeit in a more evil costume.
Red-Mist is this to Kick-Ass, especially in the comics. While Dave was inspired by the heroes in the comics, Chris was inspired by the villains (even quoting The Joker before setting up his Avenging the Villain story-line in the sequel).
In the Archie Comics' Sonic the Hedgehog series, Sonic has a direct evil counterpart in the form of Scourge the Hedgehog. Unlike Shadow, who often acts as a foil to Sonic, and Metal Sonic, which is a robot built to serve Dr. Eggman's diabolical purposes, Scourge is literally an evil counterpart: He is Sonic from a parallel dimension, where the protagonists and villains switch roles. In the early days of the comic, Scourge was simply known as "Anti-Sonic" and was identical to Sonic save for sunglasses, a black leather jacket, and a Jerk Ass attitude. More recently, Scourge has differentiated himself with a new moniker, a new green color, and a personality that is much, much more malicious than before.