In Toy Story 3, it turns out Lots-o'-Huggin' Bear used to be just like Woody. He was the favorite toy of a little kid who enjoyed her toys, Daisy being like Andy, and he was the leader of a small but loyal posse of other toys who would always lend a hand. On top of that, he has all the intelligence, resourcefulness, and planning skills of Woody. Where he and Woody diverged is their response to being separated from their respective owners, and arguably, what happened with their owners when separated. In the original Toy Story, when Woody and Buzz go missing and Andy finds out, Andy frantically searches for them until they return, and they never give up hope.When Lotso goes missing and Daisy finds out, her parents buy another Lotso and call it a day. This causes Lotso to snap and completely lose his faith in people. He then goes to Sunnyside Daycare, gathers allies, and becomes a dictator. If Woody had turned evil and bitter, he would've taken the same strategy: Gather allies, then gather power in anticipation of any upcoming threats.
Preceding Lotso is the Big Bad of the second half of Toy Story 2, Stinky Pete. Both he and Woody were part of the same toy series and shared similar apprehension about their longevity and a similar enmity to Space Toys. But while Woody decides not to abandon his friends or Andy, Pete will stop at nothing to get to Japan.
And of course, Sid was Andy's evil counterpart.
Chick Hicks, the main villain of Cars (also by Pixar) is actually the evil counterpart to Lightning McQueen. Both are actually portrayed as mean and arrogant racecars who cared about nothing but themselves and made fun of other cars. What makes them different is that at the end of the film, McQueen ends up losing the final race but is now respected by the other cars since he actually now learned to accept defeat by helping another racecar, Strip "The King" Weathers, cross the finish line after he was crashed by Chick, while Chick ended up winning the same race but is ultimately betrayed by everyone else since they found out about what he did to The King, and that doing such is actually against the racing code.
Also, Tigress and Tai Lung. Both don't know their real parents (one was raised in an Orphanage of Love, the other was a Doorstop Baby). Both only wanted their father/teacher's love. Like Tai Lung, Tigress believed she would be chosen as the Dragon Warrior by Oogway, and resented Po for 'stealing her thunder.' They also both suffer from Pride and a bad temper. Only the fact Tigress remained honorable and chose to become an even better and more worthy warrior (and, most likely, her defeat at the Thread of Hope) kept her from following the same path.
Po and Shen in part 2. Both have issues with their parents, both are real animals likened to mythical beasts (Po is the Dragon Warrior, Shen the peacock with his fascination with fire is clearly meant to be a phoenix) and they both have Failed Attempt at Drama moments.
The Princess and the Frog has Facilier (evil, male, tall, slim, young, attractive, slick) and Mama Odie (benevolent, female, short, pudgy, very old, hard of hearing and a goofball). Originally Facilier was supposed to be Odie's son.
Who Framed Roger Rabbit: Judge Doom to Eddie Valiant; both are law enforcement who hold a certain hatred towards toons. However, deep down, Eddie holds a certain fondness for toons, suppressing it mainly becuase of his brother's death and is still a good person underneath. Doom's hatred is perhaps more intense, which is ironic as he turns out to be a. toon himself.
In Kill Bill, Elle Driver, aka California Mountain Snake, is the counterpart to Black Mamba.
Rene Belloq from Raiders of the Lost Ark is a classic example. Both he and Indy are successful Adventurer Archaeologists with the main difference being that Belloq is willing to work with anyone, (including the Nazis) on a job, and that he's perfectly content to let someone else find the treasure, then steal it from them at gunpoint. Belloq also delivers an excellent example of a Not So Different speech at one point.
Ivan Vanko in the sequel is a better example. He's just as smart as Tony, and his father helped Tony's father build the first ARC reactor. Growing up in a Soviet gulag can't be good for one's personality. He ends up building his first portable ARC reactor in his rundown apartment. With his own box of scraps.
Captain America: The Winter Soldier: The Winter Soldier has many similarities to the Captain himself; both are soldiers, both have been empowered with science and both operate under orders of a larger organization (technically the same organization, as it turns out). Furthermore, both fought in World War II in the same unit but were cryogenically frozen (though Captain America stayed conscious after being revived, but the Winter Soldier was thawed and re-frozen as he was needed).
Scaramanga: At a million dollars a contract I can afford to, Mr Bond. You work for peanuts, a hearty well done from her Majesty the Queen and a pittance of a pension. Apart from that we are the same. To us, Mr Bond, we are the best.
Push has two. Nick's counterpart is Victor, and Cassie's counterpart is the Triad Watcher. Victor is a better Mover than Nick, and the Triad Watcher is a better Watcher than Cassie.
It seems to be implied that Nick and Cassie are every bit (if not more) powerful, but are novices at actually exercising their powers compared to their more experienced counterparts.
That, and the fact they are son and daughter of the best mover and watcher anyone has ever seen (Cassie's mum set up events for ten years in the future) so they may have genetically inherited a bit of it. The agent pusher is also a counterpart of the experiment survivor, although she could arguably already be better.
In Star Wars, Darth Vader is naturally the evil counterpart to Luke Skywalker (a living incarnation of the evil that Luke is perfectly capable of), and Emperor Palpatine is an evil Force mentor version of Yoda.
In the prequel trilogy Yoda and Palpatine reprise their roles as Big Good and Big Bad masters of their Force sides and actually get to fight one on one. Their battle happens simultaneously with Anakin (now officially Darth Vader) and Obi-Wan's who became evil counterparts as the only confirmed living students of their respective Force sides and former comrades. In some ways it could be said that Dooku and Mace Windu were counterparts as well, though they never had a chance to fight, in that they were the public figure who acted as the right hand and enforcer of Yoda/Palpatine.
Star Trek: Nemesis had Shinzon, the evil clone of Jean-Luc Picard whose main purpose in the story is to show what Picard himself could have become had he grown up under more oppressive circumstances. Picard himself uses this in an attempt to demonstrate that Shinzon had the choice to become a better person, while Shinzon wanted to prove that Being Tortured Makes You Evil.
In the Heisei series, Godzilla gained an Evil Counterpart in Space Godzilla, a being created from a fusion of Biollante (who was a fusion of Godzilla's DNA and rose DNA) and a crystalline entity. While Godzilla was in neutral "force of nature" mode, Space Godzilla was definitely malicious and evil, coming to Earth to torment Godzilla and conquer the planet.
An even earlier example of this would be King Ghidorah, especially in the Heisei incarnation in Godzilla vs. King Ghidorah. Both started out as creatures (A Godzillasaurus and a trio of Dorats respectively) who got mutated by a nuclear/atomic explosion. However, whereas Godzilla became an unstoppable "force of nature" that can't be controlled (at least, not unwillingly), Ghidorah remained under the control of the Futarians (a group of people, and an android, from the future who wanted to prevent Godzilla's existence and use Ghidorah to destroy Japan).
In the Showa era, while both are giant destructive monsters, Godzilla destroys merely out of his hatred of humanity and will (reluctantly) ally himself with them against bigger threats to his territory. Ghidorah, on the other hand, merely destroyed cities (and wiped out life on planets) out of sadistic glee.
Destoroyah. Both were mutated by superweapons. Both have a breath attack. Both are semi-aquatic life-forms. The difference? Destoroyah is purely and utterly sadistic taking great pleasure in killing anything and everything in sight. Godzilla, on the other hand, will protect the earth (including the humans he hates) from greater threats.
Barbossa vs. Davy Jones and Jack vs. Beckett (his old nemesis) in the third.
Maccus, Mercer and "Quartermaster" are Evil Counterparts to Gibbs.
Bosun, also, in the fourth film is also one to Gibbs, and Blackbeard is this to Barbossa.
In Black Swan, Lily might be this to Nina. Nina frequently hallucinates a phantom doppelganger that seems to mean her harm.
This mirrors Swan Lake, the ballet the film is centered around; Odile the Black Swan, is this to the White Swan, Odette.
According to Jordy, the Bread-Squeezer is this to Jason in Mystery Team.
Glory has the Negro irregulars to the 54th Massachusetts.
Transformers: Dark of the Moon plays with this. Sam and Bumblebee are given dark counterparts in the form of Soundwave and Dylan. Bumblebee came to Sam for help, Sam's family having a history with Cybertronians. Likewise Dylan's dad received Soundwave as a "client", as the Decepticon had him crunch numbers to make further trips by NASA to the moon improbable, ensuring no one would ever find the Ark. This becomes a case of Fridge Brilliance in the final battle, where both human and Autobot kill their respective counterparts.
Dylan Gould: (to Sam) Do you really think you were the first one recruited to join the "noble" alien cause?
The Dark Knight. Batman & The Joker are both described as having no limits. The former crosses merely judicial limits, the latter crosses limits that are moral.
You could say that General Zod is this to Superman too or at least to a lesser extent. What with having the exact same abilities and learning to control his sensitivity to the Earth's sounds and atmosphere. He's even able to use heat vision later on in the movie. but other than that they don't have a lot in common.
The Jaegers and the Kaiju in Pacific Rim. Both are split into one through five classes and are so large that they need two brains to fully operate. Whereas the Jaegers are used to protect humans and the cities, the Kaiju are used to kill and destroy everything in their path.
Doc Holliday and Johnny Ringo in Tombstone. Holliday is Wyatt's lancer, Ringo Curly Bill's dragon. They are both highly educated, charismatic death-dealers and death-seekers.
Each installment of the Spider-Man Trilogy has a villain who parallels Spidey in some fashion:
Spider-Man: The Green Goblin and Spider-Man gain their powers as the result of experiments at OsCorp, and the Goblin even tries to recruit Spidey with a Not So Different speech. The key difference is that Spider-Man uses his abilities to help people, while the Green Goblin uses them to exact bloody vengeance on the people who have wronged him in the past.
Spider-Man 2: Much like Peter in the first movie, Otto Octavius is transformed into Doctor Octopus as the result of a Freak Lab Accident, and is subsequently motivated by the death of a loved one. But while Uncle Ben's death pushes Peter to become a hero, the death of Otto's wife drives him mad with grief and causes him to become a murderous psychopath.
To drive the parallels home, earlier drafts of the film had Octavius as a much younger man closer in age to Peter and Mary Jane.
Spider-Man 3: They don't really come much more straightforward than Venom, who has the same powers as Spider-Man and wears a black variant of the hero's trademark costume. Additionally, in his civilian identity, Eddie Brock starts off as a rival photographer who is employed by the same newspaper as Peter.
The Amazing Spider-Man 2 effectively shakes up the classic dynamic between Spider-Man and the Green Goblin by making Harry Osborn the Goblin from the get-go, and playing up his similarities to Peter. In addition the being the same age as Peter, Harry gets pushed into his Start of Darkness by the death of his father figure, and he eventually gets his superpowers from a self-inflicted dose of the same spider venom that gave Peter his abilities in the first movie.