King Dedede and Dr. Escargon/Escargoon of Kirby of the Stars have several episodes dedicated to themselves like "Escar-gone" where nobody recognizes Escargoon due to the effect of Boukyakku/Erasem being inside his body and "Sweet & Sour Puss" where Togeira takes away Dedede's ability to get angry and makes him stay calm and friendly through all of the pain inflicted on him by everyone else just to store his anger for one big crazy mega-attack.
After being blown away by Luffy, the One Piece anime spent two episodes following Buggy around as he tries to retrieve the rest of his body and find his crew. This was, at first, a story cover-arc in the manga, but was important enough to warrant the anime to expand on it.
Other villains (Or members of a Quirky Mini Boss Squad) are given their own cover-story arcs; 'Django's Dance Carnival', which shows Black Cat Pirate Django the Hypnotist joining the Navy, 'Hatchi's Sea-Floor Stroll' where Arlong Pirate Hatchan the fish-man becomes a Takoyaki salesman, 'Wapol's Omnivorous Hurrah'...the list goes on. They also combine these with Villains Out Shopping.
In the anime version, Tier Harribel of Bleach got one of these in the form of a Whole Episode Flashback, largely to make up for the fact that in the manga, she's one of the only Espada ranked among the top 6 out of 10 that doesn't either get a fair amount of Character Development or a flashback explaining their motives. This episode ended up turning her from possibly the least developed Espada to one of the most developed.
Zenigata (who is a Hero Antagonist) in Lupin III has a television special (Lupin III: Crisis in Tokyo), focusing more on his daily activities as the inspector in the Tokyo Metropolitan, and his successful efforts in arresting a criminal far worse than Lupin. This is also one of the few television specials where he is not as Butt Monkey-ish, but more focus is given on his Bad Ass aspects.
Big Revival! We're the Heroes?! stars Zapper Zaku, Grappler Gouf, Destroyer Dom and the Zako Soldiers as they reorganize and try to take over the Gundamusai after their capture at the end of season 1. They are suitably repelled by the Gundam Force.
Genkimaru; Samurai Number One! features that same gang wandering around Lacroa's caverns after they fell from the Gundamusai. Meanwhile, Bakunetsumaru discovers Talgeese, thought to be killed by Demonic Possession.
Any early filler episode of Dragon Ball Z features Vegeta and Nappa interrupting their journey to Earth to stretch their legs. They land on a planet of insect people ruled by a tyrant, and allow themselves to be thrown in his arena for their own amusement. They depose the king and leave as heroes - until Vegeta decides the planet won't fetch a decent price and vaporizes it. Just as the Starcrossed Lovers were reuniting.
Mark Waid's run on the book also included an issue in the same manner, which served as a prelude to an entire arc featuring Doom.
Issue 4 of Johnny the Homicidal Maniac ended with Johnny successfully dying at last. The next issue was all about two of his prisoners trying to escape the Torture Cellar, with Johnny himself only appearing in a few panels at the very end.
Not really. It would be more accurate to call this trope "Antagonist Episode", but that just didn't have the same ring to it.
Although Astro City does not have a regular hero per se, the Eisner Award winning story "Show 'Em All" is devoted to showing a typical superhero tale from the villain's perspective.
And "The Voice of the Turtle" detailed the life story of Anti-Villain Mock Turtle.
Another issue is devoted to a shapeshifting alien spy, who is deciding whether or not he should give a go signal to invade the Earth. He does.
Despite technically being the Samaritan Special, one issue concerns Samaritan's archenemy Infidel far more than his heroic counterpart.
One issue of Superman had a fairly brief sub-story in which Lex Luthor thought-balloons about what to get his little nephew Val (apparently part of an estranged family) for his birthday. His Mooks speculate about what scheme he's working on as Lex demands not to be disturbed in his laboratory, figuring he's coming up with a way to defeat Superman or take over the world. Lex then dodges police as he surreptitiously delivers his invention to Val's doorstep, and is caught and led away to jail immediately afterwards. Val opens the mysterious package to discover someone has given him a Superman cape that even stretches like the real one. Val is thrilled, but at the end says, "Too bad it isn't a Batman cape. He's my REAL hero."
There's also the comic book Lex Luthor: Man of Steel, which goes into Luthor's motivations for opposing the unknowable alien whose effortless superpowers make a mockery of mankind's efforts. Subverts the 'makes them sympathetic' aspect, however, in that while we've gotten a glimpse into how Luthor thinks and what would seem to be a more sympathetic approach to his worldview, it's still made pretty clear that he's evil, and all the worse for it because he's deluded himself into believing he's righteous.
An issue of Green Lantern, intended to be a prelude to Blackest Night, shows us what William Hand's childhood was like and how he eventually became the supervillain Black Hand. The main books in the Blackest Night saga focused on Black Hand's thoughts on each of the emotional spectrum corps at the end of each book in a feature called the book of black.
Dark Reign was basically one long villain episode for Marvel.
The Dark Avengers concept was specifically revisited in New Avengers #18, which centered around Norman Osborn assembling a new incarnation of the group and forging bonds with HYDRA, A.I.M., and the Hand. Not a single hero — much less an actual member of the Avengers — appeared in the issue.
Marvel put out a series of one shots celebrating Captain America's 70th anniversary. Each one-shot starring one of Cap's allies. However two of these one-shots star two of Cap's villains. One has Crossbones as the protagonist and the other has Batroc the Leaper.
A planned miniseries for ATLAR would have introduced and developed Azul, the series' Big Bad, leading up to her main-series introduction in the eighteenth chapter, which would've been entirely from her perspective.
Queen Of All Oni already has Jade as a Villain Protagonist, but chapters still tend to be evenly mixed between focusing on her and on the J-Team's attempts to stop and capture her. Then comes chapter 10, where aside from two very short cameo scenes, the heroes don't show up at all, and the chapter focuses on Lung's attempts to break Jade to his will, and Left and Right's attempts to save her.
The following chapter, the heroes likewise barely appear, as the plot focuses on Drago's attempts to alter history in his favor — the heroes do eventually confront him, but only after he's spent the entire chapter dealing with Karasu and Blankman. The rest of the chapter deals with The Queen consolidating her hold on Jade's mind, and Jade herself recovering from the previous chapter's events.
In Perfection Is Overrated, the chapter "A Common Enemy Without A Common Cause" focuses on the SUEs (Parody Sues who are in opposition to the Himes), specifically what would have happened if they had been forced to work together. They end up killing each other before they even encounter the Himes.
"Nightmare House", which involves Nightmare Eclipse and her Psycho Rangers discussing an attempt by Eclipse to find a Nightmare of Rarity and failing, then her interacting with Nightmare Mirror. In a twist, we're shown them trying to imitate their old lives to some degree...and failing due to what they've become.
In a Russian movie The Secret of the Snow Queen, said Queen has many in-built episodes in which her personality is explored.
The 87th Precinct novel He Who Hesitates is told from the POV of the murderer with the cops who are the usual protagonists of the series only appearing when they cross the killer's path.
VISSER, of the Animorphs series, is a book written from the perspective of Edriss Five-Six-Two, better known Visser One (the first one; the Yeerk that infests Marco's mother). Individual chapters of Hork-Bajir Chronicles are written from the perspective of Esplin Nine-Four-Double-Six, the Yeerk that would later become Visser Three (and, even later, the other Visser One).
In the first-person Everworld series, there is a book called Inside the Illusion, the ninth in the series. It focuses on the main antagonist, Hot WitchSenna Wales.
The Night Watch series novel Day Watch centers upon and is told from the perspective of the members of the Day Watch, who would be the bad guys of any other series. Anton and the other Night Watch protagonists are relegated to secondary roles.
In the Sword of Truth series, a novel called "The Pillars of Creation" deals with two half-siblings of the main protagonist. He has no idea they even exist until they meet towards the very end of the book, when the main cast shows up to interact with them. The only main character of the series to show up in the novel at any point up to that is the main antagonist (to manipulate the half-siblings) and the First Wizard, who blows uphalf the big bad's army in one scene. But, other than that one scene, the novel was the second-worst of the series.
For The Wheel of Time the short story "River of Souls", comprised of material cut for pacing and worldbuilding reasons from the final booknote it was felt to be jarring to jump to a POV halfway around the world during the beginning of the Grand Finale, and also since it took place in a region Robert Jordan had only loosely outlined, Brandon Sanderson had to do a lot more worldbuilding than normal for it as well, that focuses on fan-favorite villain Demandred and deal with his rise to power in Shara.
The Darth Bane trilogy was largely an example in that it revolved around the titular Sith Lord and his apprentice. Similarly the novel Darth Plagueis revolved around the Sith Lord and his apprentice Palpatine.
Stargate Atlantis shows the POV of a Wraith named Michael in the eponymous episode, which makes the main characters look morally ambiguous if not downright evil for their treatment of the Wraith-turned-human. The sympathies of the audience remain with Michael during most of the episode, and for a large part of the fanbase, well after Michael became a threat to the team in his own right.
Babylon 5 episode "The Corps Is Mother, The Corps Is Father", which focused on Bester and the Psi Corps. The opening is even modified replacing the Babylon 5 shield with the Psi Corps insignia.
The new Battlestar Galactica episode "Downloaded" for the Cylons, and later an entire villain movie ("The Plan"), focusing mainly on Cavil.
Also the aptly named Villains in Volume 3, which served as backstory for that volume's Big Bad and expanded it for a few other characters.
The Undeclared series finale episode Eric's POV does this for the most part, focusing on the protagonist's main rival and his girlfriend's ex-boyfriend Eric and his friends. The protagonist and his friends are given subplots and Eric is fleshed out.
In Star Trek: Deep Space Nine, a couple of episodes are concentrated on Jem'Hadar, the Dominion soldiers. And there is one episode where we concentrate on Damar and VU-s... and shortly afterwards Damar makes a Heel-Face Turn.
The Criminal Minds episode "True Night" is arguably an example of this, as it has about 75% of the screentime going to the killer. We don't even get to see the BAU deliver the profile, which is otherwise a Once per Episode occurrence. Instead, we see the different parts of the profile on a whiteboard in the police station when the killer is brought in.
Once Upon a Time has some episodes centering on the villains' pasts, and they're definite Sympathy for the Devil moments. Rumpelstiltskin took the powers of the Dark One to save his son from being taken as a child soldier, and Regina the Evil Queen lost the man she loved when Snow White accidentally revealed the secret to Cora.
In the fourth-season of The Walking Dead, episodes "Live Bait" and "Dead Weight" focus entirely on the journey of the Governor post Woodbury.
There are six points of view available in Suikoden III, slowly added as you get further into the game, one of which only becoming unlocked upon beating the game with all 108 characters. The final POV focuses on the villains of the story, and what they were up to throughout the game's events. It's actually really interesting, and strikes a good balance between making the villains seem sympathetic while retaining their status as clear villains.
Chapter 3 of Mother 3 qualifies as one. It parallels the events of Chapter 2, but is from the villain's (primarily Fassad's) point of view. The Pigmasks that were enemies in Chapter 2 are perceived as allies in Chapter 3... that is, until Salsa gets set free. A lot of the cutscenes in Chapter 2 are repeated in Chapter 3, sometimes with modifications.
Dishonored has "The Knife of Dunwall" and "The Brigmore Witches" DLCs, which focuses on Daud, Corvo's Evil Counterpart and the Empress' assassin.
Subverted in the Ryder White DLC for Dead Island. In the main game he's the final boss basically on account of losing his head and injecting himself with the so called cure, only to become infected. When playing as him we learn that he's after the cure for his wife despite under orders to kill her, only for her to become infected and die. He's essentially a villain in name only.
Done a few times in the Resident Evil franchise, not counting the non-canon Mercenaries minigames:
Resident Evil 2 let you play as HUNK of the Umbrella Security Service and follows his escape from the sewers after Birkin destroyed his unit in the beginning of the game.
Strong Bad Emails on Homestar Runner started out as this; they became so popular that they ended up eclipsing the original concept of the site and turned Strong Bad into a comic Villain Protagonist. Although some of the emails are just Strong Bad making fun of other people, other times they go more into Strong Bad's personal life, such as his relationship with his whiny brotherStrong Sad.
Emergency Exit does this for Kyran and the 'villains' from time to time.
Sluggy Freelance did this with the "Meanwhile In The Dimension Of Pain" strips. Depending on where you place Oasis on the Good/Evil scale, the "Phoenix Rising" story arc might also count, and the appropriately named "Year in the Life of a Villain" arcs focuses around Dr. Schlock and Hereti-corp.
Homestuck: The Midnight Crew Intermission, which focused on the alternate universe counterparts of the Big Bad and his cohorts. We are later given a proper one after Jack murders John and Rose's parents.
There's also the Doc Scratch intermission.
Act 6 Intermission 4 follows Caliborn, who is the Big Bad Lord English before he became so big. Still pretty bad though.
Voodoo Walrus has regularly shot back to stand alone pages and entire storyarcs following baddies Mac and Shmeerm. These always stand apart from the more regular pages in that the sex, violence, language, and mayhem are all turned up to eleven.
Archipelago has one in the fifth chapter, entitled Snowflakes. It centers around the Captain Snow going and finding his (equally evil) wife and child. The chapter constantly zig zags between Pet the Dog and Kick the Dog moments, with Snow showing genuine concern for his child, then asking whether or not same child has tried to burn down the school.
The first season of lonelygirl15 included a three part villain story, "Subjects Apprehended"/"Psychological Torture"/"Communication Terminated".
The Whateley Universe has done this several times. The story "It's Good to be the Don" centers on Don Sebastiano, the head bad guy of the Alphas at Whateley Academy. "Ask Not For Whom Belle Tolls" centers around four supervillains at the school who have some problems of their own to handle - like covering up a murder. "Bad Seeds" focuses on a campus club that you can't get into unless you're the child of a supervillain.
In all three, Karma is both swift and merciless. Interestingly enough, the Bad Seeds are all Ineffectual Sympathetic Villains at worse, though Jobe is competent. Jadis herself wants to be a hero!
AH.com: The Series did this twice, once with the "Counterfactual" three-episode miniseries in Season 2 and then again with the episode "Whatever Happened to the CF.netters?" in Season 5.
In Worm, the author regularly writes "Interludes," scenes told from a perspective other than Taylor, and never uses the same character for an interlude. Thus, interludes have involved supervillains, superheroes, civilians, or none of the above.
The Teen Titans episode "Lightspeed," which features the H.I.V.E.F.I.V.E. and Madame Rouge from the Brotherhood of Evil. Kid Flash, a minor hero, is also prominent. Notably this episode also serves as a vehicle for Jinx's eventual Heel-Face Turn.
Invader Zim inverts this with several episodes that focus on Hero Antagonist Dib rather than Villain Protagonist Zim, with a few episodes leaving Zim out altogether. One could argue this happens so much the show has two protagonists, breaking the usual hero/villain mold.
Also "Game Slave 2," which focuses on Gaz rather than Zim or Dib. She's not technically a villain...but she's pretty close.
The third season premiere of The Venture Bros. centers almost entirely on The Monarch, Dr. Girlfriend and their respective Mooks, only briefly involving Dr. Venture and Brock Samson, neither of whom have any lines. The title characters are nowhere to be seen, and are even replaced in the opening sequence by the Monarch and Dr. Girflriend Mrs. the Monarch.
Batman: The Animated Series had a couple. "The Man Who Killed Batman" followed a two-bit thug who was thought to have killed Batman, while the titular hero was obviously absent through most of the episode. "Harley and Ivy" was basically "The Harley Quinn and Poison Ivy Show" with the Joker as the guest star. "Almost Got 'Im" also qualifies.
Batman The Brave And The Bold goes one step further giving the Joker his own episode complete with a cold open where he destroys the future earth (with an appearance from obscure DC character Kamandi), his own title sequence renaming the show "Joker: The Vile and the Villainous" and a plot featuring him teaming up with obscure DC villain The Weeper against Batman.
The Powerpuff Girls episode "Just Another Manic Mojo" features Mojo Jojo going through a normal day - which, for him, consists of getting breakfast, reading the paper, and plotting to destroy the titular heroes. The Powerpuffs themselves show up later on, but the focus still remains on Mojo.
In "Custody Battle" he and Him fight over who gets to be the father of the Rowdyruff Boys and in "Prime Mates" he has to deal with Mopey Popo (the girls appear briefly in the latter).
Later on there's "Crock Talk", focusing on Crocker gaining notoriety through his online talk show.
The Phineas and Ferb episode "Hail Doofania!" turns the show's usual formula on its head by focusing on Doofenshmirtz's daily scheme, inverting some of the lines (Phineas spouts the "entire tri-state area" line, Norm asks "Whacha doing?"), and instead of Phineas and Ferb's plan for the day being disposed of by Doofenshmirtz's invention, their invention disposes of his.
Samurai Jack had "Aku's Fairy Tales" where Aku, tired of all the hero worship Jack gets from the children, decides to tell stories with him as the hero and Jack as the villain. Jack himself only shows up in these stories.
Two more showed up in the final season. "The Princess and the Bounty Hunters" concerned an Anti-Villain bounty hunter who convinces several others to gang up on Jack to capture him. Jack shows up near the end and defeats them easily. Another, "The Tale of X9", involves an old robot of Aku's with a Personality Chip forced to go after Jack after Aku steals the only thing he cares about. As you could expect, it doesn't end well.
Dexters Laboratory had two episodes devoted to Mandark. The first centered around his attempts to impress Dee Dee in a surfing contest, with Dexter not appearing at all. Though the effectiveness of that episode wavers a bit considering, other than using his science to cheat in a surfing contest, he wasn't up to anything particularly villainous. The second was pure Villains Out Shopping, with Mandark going through his morning routine to the meter of his Evil Laugh before going out to battle Dexter.
Taken one step further when a set of shorts were all dedicated to Mandark — even the intro was altered with Mandark electrocuting Dexter instead of Dee Dee and the usual Dexter's Laboratory title card reading Mandark's Laboratory. Though Dexter does get back at him by the end of the show when he tricks Mandark into electrocuting himself much like Dexter in the intro.
The Boondocks gives us "The Uncle Ruckus Reality Show" and "The Story of Jimmy Rebel", both of which star Boomerang Bigot Uncle Ruckus (no relation) and relegate the Freeman family to minor supporting roles. The episodes usually try to portray Ruckus as a slightly sympathetic figure (but only slightly). In the first, his self-hatred almost drives him to commit suicide. In the second, meeting him convinces a No Celebrities Were Harmed version of Johnny Rebel to give up anti-black music (but not racist music).
"Hun on the Run" focuses on Hun as he tries to rescue Karai from Bishop.
Star Wars: The Clone Wars had an episode entirely from Asajj Ventress' perspective, followed by two more that also focused on Dooku and Savage Oppress. Jedi only appeared in supporting roles.
Storm Hawks episode "Power Grab" focuses entirely on the main villains of the series. Master Cyclonis and the Dark Ace leave Cyclonia in Ravess' hands while on a mission, and her obsessive control drives her brother and fellow commander Snipe to take command from her. However, his idiocy drives Psycho for Hire Repton to take over, and then his brothers. Through it all, a nameless Talon commander tries to get the rank and prestige he wants.
Aqua Teen Hunger Force has "The Last One", which focuses on the Mooninites gathering together every villain in the series so far, to destroy the Aqua Teens. Predictably, all of them fail miserably.
In Ultimate Spider-Man, "Me Time" ends up being this for Doctor Octopus. The episode focuses on Doctor Octopus trying to capture Spider-Man himself lest he be played off by Osborn, showing him winning the fight between Spider-Man, as well as implying that his Evil Cripple condition has taken a toll on his appearance, hygiene, and sanity. Before this episode, Doctor Octopus was scarcely seen except in scenes which are in his lab.
The Gargoyles episode where Xanatos struggles to save Fox after he gives her the Eye of Odin as a gift to seal their relationship. Fox turns into a werewolf and Xanatos is shown for the first time with worry and panic, something he's not known for. Ultimately, it serves as an episode to reveal that Xanatos is not the ruthless villain he wants people to belief, because he's capable of loving someone besides himself. The episode foreshadowed his Heel-Face Turn at the end of the second season.