Later subverted with his Jumping Off the Slippery Slope in "Cold Comfort." Though his actual final appearance before Batman Beyond (an issue in the comic Gotham Knights) didn't even have him commit any crimes, instead, the crimes pinned on Mr. Freeze were actually done by a robotic duplicate made by Nora's stephusband, and Freeze even pulled a Heroic Sacrifice in the end.
In his Batman Beyond appearance, he tries to kill hundreds of innocent people to get vengeance on two, but in the end pull an Enemy Mine with Batman when Blight unveils himself, and sacrifices himself to tell Batman to get out of there when the facility was collapsing. In the end, Freeze goes back to being an Anti-Villain.
Terry: Freeze! We have to get out of here! This whole place is coming down!
Freeze: Believe me, you are the only one who cares.
Freeze is far from the only Batman villain to feature this trait. There's Catwoman, who is a Classy Cat-Burglar, definitely a criminal, but far from a violent psychopath like most of his other enemies. She's frequently portrayed sympathetically and is a major (many would say, THE major) love interest for the hero, sometimes nudging her into Anti-Hero territory.
Matt Hagen, AKA Clayface, is an actor-turned-shapeshifting monster whose main purpose is to get back to looking human again and get revenge on the people who turned him into Clayface. It was partially his own damn fault that he got mixed up with them, but don't expect him to acknowledge that. He ends up Jumping Off the Slippery Slope in The New Batman Adventures, though, and unlike Mr. Freeze, doesn't recover from it.
The Riddler has shades of this as well in several incarnations, considering, most of the time, his entire gimmick is based on pathetically making it easier for Batman to catch him, and his crimes are relatively benign ones...right about now, he's spending more time reformed than not. Notably not the case in the DCAU where he successfully takes the level in bad-ass and has intentions that (while sympathetic) are clearly murderous.
The Mad Hatter is also sometimes quite sympathetic, and not only in the Animated Series (though his first appearance therein is filled with enough squick to make everyone feel comfortable when he gets repeatedly punched in the face). At one point in the comic based on the Animated Series, he trapped Batman in a morally simplistic Silver Age dream world...and when Batman managed to free himself and confront him, the Mad Hatter explained that he thought it would make the ordinarily lonely and brooding Batman happy for once. This plot was used in "Perchance To Dream".
Hatter: You ruined my life! I was willing to give you whatever life you wanted, just to keep you out of mine!
Killer Croc was this for a time, committing crimes to get food and clothing for homeless outcasts who he sympathized with as they, like him, were hated and shunned by society.
Then we have little Mary Dahl, a 30-something actress who is trapped in the body of a 5-year-old due to a rare genetic defect. After failing to be taken seriously as a dramatic actress as Macbeth's wife in a stage play, she snaps and reverts to her TV persona, going so far as to capture her old castmates to re-create a birthday party episode "ruined" by Cousin Oliver (according to script, of course). Seems standard fare...but then they hit the hall of mirrors when she tries to escape from Batman. A bit of mind breakage is kind of expected, in a situation like that.
Mary: (sobs) I didn't mean to do it.
Terry gets his own Dating Catwoman moment with Ten, member of Beyond's version of the Royal Flush Gang. She's significantly more reluctant and less ruthless than the rest, acting more out of familial loyalty than malice or greed. At the end, we get the delightful Continuity Nod from Bruce:
Terry: This kind of thing ever happen to you?
Bruce: Let me tell you about a woman named Selina Kyle...
Two-Face/Harvey Dent. Granted, in Batman: TAS, he had the split personality beforehand...but then, the guy suffers from a split personality!
The Penguin entered this territory in the episode "Birds of a Feather". He decides to reform and actually goes through with it. Two socialites decide to play a trick on him and the female one pretends to be in love with him; but the Penguin takes it seriously and saves her from muggers. Ultimately, though, he finds out about their original intentions to mock him, snaps, convinced that society will never accept his reform, and kidnaps her. It seems to go without saying that attempting to make a Butt Monkey of a recently reformed criminal is a VERY bad idea.
About the only really heinous thing about Harley Quinn is her undying crush on the Joker. When she isn't around the Joker, she's still an obnoxious Tsundere, but she rarely tries to harm anyone unprovoked, and she legitimately cares about a few others, such as Poison Ivy (mentioned above) and her pet hyenas.
Arnold Wesker, aka the Ventriloquist, is a calm, quiet person bossed around by his other personality, Scarface.Fortunately, in "Double Talk" he finally gets rid of Scarface for good, making him one of the few Batman villains to successfully reform.
Black Cat fills precisely the same role she had in the comics. Unlike her comic book counterpart, she never made the jump to Anti-Hero since the show was cancelled before this could transpire.
Sandman was definitely an anti-villain, as explored in season two. In his own words: "I never meant to hurt anybody; I was just in it for the bucks".
Electro started out as this, as he was a decent guy before his accident and was just trying to get a cure so that he could have a normal life. Eventually though, With Great Power Comes Great Insanity kicked in, and he began to actually enjoy his new evil persona.
Molten Man revisits the Electro angle and plays it a little straighter - the only reason Mark Allan is a villain at all is because his transformations are outside of his control and the deal is "fight Spider-Man or stay that way." He has nothing against Spidey, no real reason to want to be a villain, deeply regrets how his transformation hurt the people he cares about, and when the opportunity presents itself he isn't even inclined to escape prison or take revenge on Spider-Man until coerced.
Even The Batman has examples of Anti-Villain such as Clayface who had his back story changed as to become horribly mind raped by The Joker after already having to deal with hell from Da Chief, and to make it worse, he was a childhood friend of Batman, and one of his few supporters on the Gotham Force.
Also the Riddler, who is even more sympathetic than usual, who only wanted to help increase intelligence only for one experiment of his to be sabotaged by his co-worker who he had a crush on.
Poison Ivy, particularly in the spin-off comic series The Batman Strikes! She just wants to make the world a better place....for plants.
Harley Quinn also counts, for all the same reasons as her DCAU counterpart.
One-shot villain Francis Grey, who was so unlucky that stealing a watch in order to make ends meet for his family caused a chain event of freak accidents that resulted in him getting locked in jail for much longer than his actual crime warranted.
For a few episodes after his Heel-Face Turn, Zuko is arguably the purest form of this trope; his attempts to explain his change of heart to the Gaang and prove the sincerity of his intent only serve to convince them that he's gone from threat to nuisance, and after he burns Toph by mistake he cries unto the heavens, "Why am I so bad at being good?!"
Mai and Ty Lee would count as either this or Punch Clock Villains, moreso Mai than Ty Lee since, while Ty Lee isn't evil at all, Mai has more of a sympathetic reason behind her behavior than Ty Lee does.
Amon lied about his backstory, but the real one isn't that much less depressing; he is a waterbender, and his father, Yakone, forced him and his brother Tarrlok to master bloodbending, and saw them as nothing more than tools for revenge. Not only would the emotional and psychological abuse by his father be enough to warp him mentally, but bloodbending too much screws with your head. This makes him even more similar to people like Adolf Hitler, since he leads a revolt against what he sees as the impurity of the world even though he is a bender himself (Some believe that Hitler had Jewish ancestry).
Scourge in Transformers Cybertron, whose iron-fisted rule over the Jungle Planet began with the intent of bringing law to a lawless world, and is about halfway down the Slippery Slope when we meet him, slips down further, then manages to claw his way back towards the top near the end of the series.
An even greater example is Sky-Byte from Transformers: Robots In Disguise, who sometimes found himself trying to protect human lives. He's also flamboyantly comical, prone to singing songs and writing haikus, and seems to desire appreciation by his commander. By the end of the series, rather than be incarcerated with the rest of the villains, he escapes to live peacefully on Earth.
Sky-Byte: "Now, more than ever before—my dear hostages need me!"
Transformers Generation 1 had at least one in Thundercracker, one of the original three Seekers. He was constantly shown to have Noble Demon tendencies, did not enjoy the suffering of humans like most 'Cons and was at times capable of compassion, and would question his allegiance (contrast his colleagues Starscream and Skywarp - one a Smug Snake backstabber, and the other a Stupid Evil psycho). It's strongly implied the main reason he continued to serve Megatron was out of fear rather than loyalty. Skyfire/Jetfire may also count, but since he underwent a Heel-Face Turn so quickly it's debatable.
Breakdown has a lot of history with Bulkhead, but they seem to share a common respect for one another, and their battles often contain a lot of Trash Talk. In addition to that, he's shown a degree of sympathy for the Mooks.
Dreadwing values loyalty and honor above all else and regards his alignment with the Decepticons to be one of duty. He displays the utmost respect for bots like Optimus Prime, and despite being a Combat PragmatistMad Bomber, isn't beyond calling a truce when both sides will benefit for the greater good. While he was planning on a Roaring Rampage of Revenge after hearing about his brother's death, he became even more infuriated when he learned about Skyquake's ultimate fate at the hand of Starscream.
Season 3 adds Predaking to the list. Something of a Proud Warrior Race Guy, he only fights for the 'Cons because they promised to resurrect an army of his extinct brethren for him to lead. They did create an army of beasts, but realized that he could use it to turn on their diminished forces, and thus hatched a plan to indirectly destroy the clones. This gives us a reason to feel bad for him, adding a bit of woobieness.
The Ultra-Humanite, as he appears in Justice League. His grand list of crimes is as follows: 1: breaking Lex Luthor out of prison and saving his life from kryptonite poisoning so that Ultra can get a huge donation to Public Broadcasting (and then foiling Lex's plot and turning both Lex and himself in once Batman gives him a better offer), and 2: planning to demolish a modern art museum during the Christmas Episode (when, of course, nobody would be around to be caught in the crossfire), only to quickly declare a Christmas Truce with The Flash and help him give Christmas presents to orphans (ok, so he modified the toy so it recited The Nutcracker, complete with musical score, instead of blowing raspberries). He isn't seen in another villain role after that.
Many (if not most) of the villains in the first season of Super Friends qualify. Goodfellow invented the GEEC so as to free mankind from tedious chores, then offered it as a free service to everyone on Earth. The ocean-polluting aliens were filtering silicon from Earth's seas for fuel, because they were stranded and their space ship ran on silicon. The global-warming aliens were heating up the Earth because their own planet had frozen overnote admittedly, by their own industrial air pollution and they needed a new home.
Demona, a mostly immortal gargoyle who has watched her species driven to near-extinction over the course of her life and wants to Kill All Humans as revenge/to protect the few that remain. Aside from her Freudian Excuse, she has her daughter, Angela, as a Morality Pet, and is generally portrayed as being deeply wounded deep down.
Macbeth is another immortal with a history with Demona, and his early actions are mostly centered on finding her so that he can finally die, since only she can kill him. Later on, he drifts more into Anti-Hero territory, though it's hard to say where he stands by the time the comic ends.
The Emir, a one-off villain associated with Xanatos, tried to control the spirit of death so that he could resurrect his young son.
Sylvester the cat and Elmer Fudd in Looney Tunes, who, beside their personal vendetta against their respective foes, are quite nice fellows and star as the good guys in one or two cartoons.
And on the Disney side, Pete was nothing more for Mickey Mouse than what Sylvester was for Tweety in his debut. While Pete is more Machiavellian these days, most other Disney villains would still able to smash him in a villainy contest. And in few instance, he, too, would have a good (if slightly anti-heroic) role once in a while.
The second Teenage Mutant Ninja Turtles 'toon has several of these, but three stand out. Karai begins as a Worthy Opponent, who, despite disagreeing with some of the Shredder’s more destructive tendencies and secretly stopping them when she can, stands by his side because he is her adoptive father. Bishop is a Well-Intentioned Extremist, who truly does care about his stated mission to protect Earth and will fall in with anyone who aids that goal. Baxter Stockman, although amoral and unrepentant, becomes one of these due to getting the short end of the karma stick during his systematical reduction to a Brain in a Jar. By the time his Day In The Lime Light comes along, he's more tragic than anything.
In Ben 10: Ultimate Alien, it's revealed that Charmcaster's villainous attempts to gain great power were all to free her enslaved home world and to resurrect her father. Unfortunately, neither one of these ended up working well for her. In Ben 10: Omniverse, she's a villain because she's recovering from a breakdown and doesn't know what else to do with her life, and is thus open to suggestion from two manipulative bastards she has under her control.
One episode of Samurai Jack is entirely from an enemy Mook's perspective. It is revealed that this robot was given emotions and that a dog he cares for is held hostage, which is why he fights Jack, only to be immediately killed.
Another episode focused on a group of bounty hunters who wanted to capture Jack. One of them, Princess Mira, wanted to capture him to trade to Aku for her kingdom's freedom.
Sargeant Hatred of The Venture Bros., once he finally enters the spotlight, turns out to be far more benevolent than his name would suggest, treating the Venture family well and not taking his position as their "arch" all that seriously. In season 4, he even becomes their bodyguard and attempts to be a good role-model to Hank. Unfortunately, he's severely emotionally unstable, not to mention a recovering pedophile, so the love is not exactly reciprocated.
In Iron Man: Armored Adventures, Gene Khan is this initially and throughout most of the first season. Whether or not he's still an Anti-Villain after the events of the season one finale is a serious case of contention among fandom. On the one hand, there's some foreshadowing that he may not be too far gone to save, and he doesn't seem happy with how things have turned out. On the other hand, he has (by the standards of Nickolodeon) crossed the Moral Event Horizon for many, given he almost killed Tony, kidnapped Tony's dad, and threw this into Tony's face mercilessly.
Madame Masque, aka Whitney Stane, is another example, especially in her second-season return.
The Jonny Quest franchise isn't known for its sympathetic villains, but Jonny Quest: The Real Adventures did a number with Ezekiel Rage, primarily in his initial appearance, where he was a delusional man, driven mad by the brutal loss of his wife and child, who mistook Jessie for a hallucination of his own daughter and wanted revenge against anyone he could find. His subsequent appearances, however, are much less sympathetic.
The titular character of Where on Earth Is Carmen Sandiego? gradually became this. She played many related tropes straight, too: the Friendly Enemy, often partnering with her rivals Zack and Ivy; the Worthy Opponent, shown to enjoy her "game" with ACME and harbor no ill feelings against them; and occasionally the Villain Protagonist, particularly in the last two episodes of the series when she met her long-lost father only to see him abducted by proper villain Lee Jordan.
Bushroot in Darkwing Duck was once described along the lines of "not so much a villain as just desperately in need of a peer group".
Arbutus from Aladdin: The Series (that guy who has power over plant life) could arguably count. He did capture Jasmine and demand her as the Sultan's twenty-year-old debt payment for killing one of his flowers, but he didn't exactly do anything particularly villainous beyond that and wasn't even evil by standard definitions.
Moordryd Payyn from Dragon Booster qualifies. It's implied rather often that while he is a jerk most of the time, he is really only doing the evil stuff for his Big Bad dad's approval (shown best in episode 11, "Pride of the Hero", when he was shocked out of a With Great Power Comes Great Insanity state when his father (under pressure from The Hero, the Dragon Booster) admits to being proud of Moordryd. From Moordryd's reaction, one must assume that he doesn't get that praise often).
Also, when things got really dangerous for the whole city (including his friends), Moordryd saved the city from the Brainwashed and Crazy Dragon Booster, foiling his father's scheme. It's also implied in the final episodes that he might go Anti-Hero, but as the second series never materialized, it's impossible to know.
Adventure Time: the Ice King may or may not be this trope. While he does make a hobby out of kidnapping princesses and is shown to have sociopathic tendencies, most of the time, he's just desperate for the same affection Finn and Jake receive but doesn't know how to get it, due to, again, him being a sociopath.
One episode revolved entirely around the Ice King spying on the duo using a creepy horse costume, not in an attempt to learn their secrets, but to learn how to have fun.
And now it's been revealed that he was once a human named Simon Petrikov until, one day, he bought an old antique crown and tried it on. It drove him insane, driving away his fiance and warping him into the Ice King we know today. He even apologises in the tape where we find this out for anything awful he might do under the crown's power.
The Earl of Lemongrab could count as this. He isn't really a villain- just a huge prick- but the extent of his jerkassery certainly paints him in a villainous light. He sent everyone in the kingdom to the dungeon for one million years, terrorized and threatened the candy people for petty reasons, made a child cry in deleted scene, belittled his butler, screamed at and imprisoned everybody including his mother... But the reason he's so insensitive and such a huge jerkass is the fact that he's a science experiment gone horribly wrong. Whatever mistake Princess Bubblegum made while creating him resulted in him having an Ambiguous Disorder that causes him a Hair-Trigger Temper, Super OCD, No Social Skills, No Indoor Voice, and the general mannerisms of The Mentally Disturbed. Sure he's a jerk, but he's also "completely unadjusted to living," according to Adam Muto, a writer on the show. To make matters more puzzling, his motivations are far from malicious- he just wants the kingdom to be quiet, peaceful, orderly, tidy, clean, and free of pranks and pillow fights. It just happens that, in his maladjusted mind, Disproportionate Retribution is the proper way of dealing with disorder of any kind.
This could be seen as a metatextual Shout-Out to Generation One; both of the two My Little Pony TV Specials featured one of these. First was Scorpan, a demonic-looking ape who reluctantly served Big BadTirak to protect his young dragon, Spike, and ultimately turned on Tirak to save Spike. Next was Rep, a lizardman who only works for Catrina because he used to be in love with her before she became an addict to witchweed potion.
In some Tom and Jerry shorts, Tom qualifies, due to him either not starting the conflict, just trying to protect the house, doing his job, or other things. At some point, the writers allowed him to win a few times.
The titular trio of Ed, Edd n Eddy. Technically they are three con artists trying to scam their peers. It just happens that Ed and Edd have stronger moral code than their targets and Eddy has a Freudian excuse, namely a sociopath older brother.
Nox from Wakfu arguably qualifies for this despite stealing the life force of hundreds of thousands of people and plants, considering how he thought that when he traveled back in time to save his family that everything would be undone. This makes it even worse for him when his plan fails, making the lives he took utterly pointless, and he's hit with such a My God, What Have I Done? that he commits suicide.
Snowman only stole Eustace and Muriel's Melting Genes and froze all of Nowhere into the West Pole in order to preserve himself as the Last of His Kind since all of his friends were melted to death by global warming. Once Courage fixes the hole in the ozone layer and revives all his dead friends in the process, he's more than happy to reform and leave Nowhere in peace.
The Duck Brothers only kidnapped Muriel to help bust their brother out of Area 51 before he's made into a duck dinner. Once Courage learns the whole story he's more than happy to assist them and they leave in peace.
Fred isn't really evil so much as he is insane and slightly NAAAUUUUUUUUUGGGHHHTTYYY, yes he does have an obsession (and maybe a fetish) for shaving people completely bald, but it's not like he ever tried to hurt anyone.
Conway the Contaminationist wanted to share his secret to a longer life with Eustace and Muriel, unfortunately his methods involved turning their home into what amounted to a landfill, it made him very healthy, Eustace and Muriel? Not so much.