In Disney's Treasure Planet, John Silver is supposed to be the bad guy; and he does it pretty well, most of the time. But he also turns out to be a great father figure to Jim Hawkins and his soft spot for the lad pushes him to do the right thing now and then. His core motivation of wanting to get what is, in his eyes, rightfully owed to him is more complex than just standard pirate-relate greed.
King Haggard of The Last Unicorn, as shown in the scene where he explains why he captured the unicorns. Not from greed, or power... but because they're the only thing that makes him happy.
Rameses in The Prince of Egypt (yes, the Pharaoh). Unlike the Pharaoh of The Bible, he's shown to be a well-meaning man who genuinely loves his brother Moses and is struggling with his father's shadow, but because of his upbringing, he's blind to certain things in life, like the suffering of the slaves. Yet he's not villainous at all until Moses starts demanding that he let his people go. The writers deliberately humanized him, but made him so sympathetic and tragic that, at some points, they had to rewrite some scenes between him and Moses because Moses came off as being cruel to him. And even then, he is a very tragic figure.
Aladdin's father in Aladdin and the King of Thieves. As implied by the title, he is the leader of the forty thieves. However, it's implied that his only motivation for wanting to lead them, as well as stealing various treasures, and why he left the family to lead them, was to allow his family to not be impoverished anymore. He also intended to return to his family once he had amassed enough wealth, but by the time he returned, he was unable to find them, and thus he believed they had died.
Films — Live-Action
Darth Vader, who in the end of the original series turns out to be something of a Tragic Monster. In the prequels we see him as an anti-villain, someone with noble ideals who is manipulated into evil means. Eventually he's consumed by self-loathing.
M starred Peter Lorre in the role of Hans Beckert, the first Serial Killer in all of film and an implied pedophile, and one of the most pitiable villains ever portrayed.
For that matter, the fraternity of criminals who take it on themselves to track him down is, at some points, almost indistinguishable from the actual police. Even to the point of throwing him a "trial", which they somewhat bleakly joke is legitimate because they're all legal experts, what with so much experience with the judicial system. Then they almost tear him apart...
Which leads to an epic Reason You Suck Speech by Beckert himself, who asks the fraternity what right they, "lazy bastards" who commit crimes for things they could have avoided if they learned a decent trade, have passing judgment on someone who is compelled by powerful impulses to do the things he does "against his will". He seems to genuinely hate himself for what he does as much as anyone else.
Samara in The Ring Two. Sure, she killed a bunch of people, but she just wanted to be loved. This is different from how she is in The Ring.
In Spider-Man 3, the Sandman is a textbook Anti-Villain, pursuing noble ends (saving his daughter's life) through criminal means.
Doc Ock in 2. Altruistic guy, working for "the good of mankind", accidentally kills his wife and turns himself into a monster with no inhibitions, and fixates on his dream, still believing that he is trying to help humanity, when he is actually constructing the means to destroy half of New York City. He's manipulated by his own technology to boot. Regains his senses at the end and pulls a Redemption Equals Death to atone for his crimes.
Prince Nuada in Hellboy II: The Golden Army. Nuada is striking back at humanity because it is destroying his world. Nuada insists, and the film supports, that the world will be a worse place without his kind. Director Guillermo del Toro notes that Nuada has more morals than most of the heroes, notably Abe and Liz, who both place their own love before the fate of the world... Although Nuada is also a hypocrite and somewhat Ax-Crazy, such that you shouldn't be outright rooting for him to win.
Fredrick Zoller is almost the most conventionally heroic character in Inglourious Basterds until his very last lines. He's brave, humble, seems like a Dogged Nice GuyRomantic Comedy protagonist while courting Shoshanna, and actually seems to have some remorse and trauma from his war service. But on the other hand...he's a fucking Nazi, and then it turns out that he doesn't like to take "No" for an answer.
In The Rock, General Hummel (Ed Harris) is an American Vietnam War hero who is motivated to get the government to acknowledge the sacrifices of soldiers who died during black ops...even if he has to hold an entire city hostage to do it. Furthermore, late in the movie it's revealed that he had no intention of ever letting innocents die, and gets killed trying to stop his Ax-Crazy subordinates from launching nerve gas at San Francisco.
The bank robbers in Inside Man are doing it to get even with a former Nazi Collaborator. They have scruples that involve not hurting or killing anyone, and not stealing cash from the bank but only some diamonds from a man guilty of war crimes. They freely admit they are no martyrs but don't fit under the label of plain old villains either.
Roy Batty was nothing if not this trope; all he wanted was a way for himself and his fellow Replicants to live longer than the four years allowed to them.
Believe it or not, Hitler in Downfall, though his actions were not exactly noble, per se. He's portrayed as a broken man. Many were offended that Hitler could ever be portrayed sympathetically, but the directors defended it by saying that they were portraying him as a three-dimensional person and not just doing it For the Evulz.
Between his paranoia, uncontrolled sobbing, and screaming that the German people all deserve to die for failing him, the directors were really trying to reveal him to be a pitiful, mentally ill waste of life, rather than a diabolical supergenius warlord which the mainstream media likes to portray him as.
The original Scarface, the one from 1932, has an Anti-Villain as its titular character, who pets the dog at multiple points in the film. It was very controversial at the time because of this.
William "D-FENS" Foster from Falling Down. He's dangerously insane and becomes increasingly violent, but at the same time he's also clearly a victim of powers beyond his control, and the audience is encouraged to feel catharsis through his actions even as the movie condemns them.
Sybok from Star Trek V: The Final Frontier uses his powerful telepathic abilities to cure people of their deepest emotional pain in order to win them over to his side and help him achieve his goals. It's unclear whether he's more motivated by altruism or selfish ends...though he achieves both either way.
The villains of The Adjustment Bureau aren't really very evil. In fact, they're trying as hard as they can to save humanity from its own evil. They just have a heavy-handed, Lawful Neutral way of doing it.
Lestat in the film adaptation of Queen of the Damned: he's a remorseless, amoral killer, but he has an incredible capacity for compassion and empathy. And, as he'd point out, he's just obeying his nature when he kills.
Chip Douglas from The Cable Guy. His creepy and obsessive stalking of the main character is driven by the fact that he's been socially isolated for his entire life and is desperate for somebody to be his friend.
Robert from Mystery Team. He didn't want Brianna's parents to be killed, and took her and her sister in. He didn't even interfere with the Mystery Team. That said, his motives are rather sinister, risking the lives of thousands of employees and customers to save money.
Loki, the villain from Thor, is continuously doing the wrong things for the right reasons. He's actually just a screwed-up "Well Done, Son" Guy trying to win his father's approval through pretty much the worst means possible.
Bill the Butcher of Gangs of New York, a violent, remorseless thug who is motivated by a powerful sense of patriotism. Though an unapologetic racist (he hates the Irish), he's still fair-minded enough to find merit in individual Irishman who he takes under his wing.
Claudia in Snow White A Taleof Terror. She is only really a villain once the miscarriage drives her mad and the enchanted mirror starts manipulating her. And then what does she want? A living child and the love of her husband.
In the 2011 film Warrior: Both Brendan and Tommy are treated sympathetically throughout the film, but Tommy fulfills the role of the villain. He's a complete jerk to both his brother and father throughout the film, refusing to help them reconcile their old family demons (although not without reason). He also fights like a classic screen villain, curb-stomping his foes with anger and brutality.
The vampires in We Are the Night are bloodthirsty killers, but are deeply tragic characters.
General Zod in Man of Steel. While he is willing to commit genocide on the human race he sums himself up magnificently in a single quote, "Every action I take, no matter how violent or cruel, is for the good of my people." He was bred to be a warrior, to defend his race no matter how monstrous he had to be to do so.
In Now You See Me, The Horsemen never harm any innocents, and the people they're stealing from have wronged many others in the past and indirectly caused the death of one man as well as cheating the family out of his inheritance.
Designated Villain Lucian in Underworld - while employing some rather dubious tactics - was a former slave who led an uprising after his lover and unborn child were brutally killed, and is only trying to prevent his people from being exterminated. If his plan in the first film had succeeded, the end result would have been peace between the two sides.
Boss Johns in the third Riddick is after Riddick, but his grudge is quite personal, since he wants to know what happenened to his son on M6-117 and if Riddick killed him. He also views Riddick as a dangerous, murdering savage. After learning that his son was a child-killing junkie, he keeps his promise to Riddick and they leave on good terms.
Major König in Enemy at the Gates is hunting down Vasily and killing his friends, but he's involved in a brutal war which naturally requires him to kill, doesn't engage in atrocities himself until he hangs Sacha (and that's for being a spy), disapproves of torture as shown when he's told of Volodya's capture, and has only come to Stalingrad to avenge the death of his son.
General Ross in the 2003 Hulk movie, as opposed to his The Incredible Hulk version. Considering the long history of Hulk comics neither is exactly inaccurate to the comics. He's portrayed as a concerned general who deeply loves his daughter and is just trying to stop the hulk menace, but goes out of his way to pursue and distrust Banner because of who his father is.
President Patel, Elysium's board of directors, and Delacourt's unfortunate assistants are repulsed by Delacourt's Establishing Character Moment (which nearly leads to Delacourt losing her job as Defense Secretary). Not that Patel's any more tolerant of undesirables from Earth, but he prefers to simply round them up and deport them.