Revy calls Shenhua at home to seek her help, and as Shenhua talks on the phone, you see her apartment mates Sawyer the Cleaner and Rotton the Wizard playing video games. Not so odd in Rotton's case, since he's a pretty decent guy, but definitely this trope for Shenhua and Sawyer, who are quite psychotic.
Since every character in the series is a Villain Protagonist, any time they are "off the job" would probably qualify for this.
MayuriKurotsuchi from Bleach is a rare "Good Guy" example of this trope. His various omake episode appearances include offering to change Renji's zanpakuto Zabimaru into an attractive woman (even providing a pamphlet) and filling in for hisdaughter at a "Shinigami Womens' Society" meeting. His character sheet, too, lists his various hobbies, which include reading every single line of the "Seireitei News Letter" and publishing his own surprisingly popular personal health article. However, a more literal example of the trope could be applied to Gin Ichimaru, who hosts his own amusing "Bad Guy" version of the Shinigami Golden Cup omake.
Gin, Tousen, and Aizen are also seen at the end of one OVA casually sipping tea in the mortal world. Gin cheerfully advises the audience to "be careful on your way home." Especially with Aizen's Moral Event Horizon...
In the 23rd ending credits for the anime for episodes 266-278, every character, villain or not, is seen in street clothes in the mortal world, participating in evening activities. Only one who defies this is, naturally, Ulquiorra; instead of doing anything, he's out in the rain in an overcoat, still looking the same. No bags, no indication of what he's doing, and no one around him. (The song is 'Stay Beautiful' by Diggy Mo, if you're interested in searching for it on Youtube - no link provided as they have a tendency to get taken down.)
A large chunk of Chrono Crusade (manga version) shows The Sinners doing strangely...normal things. Aion goes out shopping for Fiore and sneaks in a gift for her. In a later scene, he discusses his evil plans with his group at what appears to be a normal family dinner. Flashbacks show Chrono and Aion drinking together, Aion teasing Chrono about his crush on a girl, Chrono doing laundry, etc. At one point, when one of the heroes is kidnapped by the bad guys, she even points out at the breakfast table that everything seems very...normal.
Arguably, Death Note and Code Geass use this as an Invoked Trope with the behavior of their respective Villain Protagonist and Byronic Hero when they are aware they are under surveillance. Light has his infamous potato chip eating scene, and Lelouch has a perhaps better example in season 2, where he goes on a sort of date with Shirley at the mall and is observed by both his fellow classmates and the government, and manages to pretend to be oblivious to both, and to enact a scheme as Zero while on the date.
And if you don't take in to consideration that MisaAmane is the Second Kira, she's actually a pretty fun person, as well as a very successful entertainer (model, Idol Singer, actress, etc). Don't cross either her or Light and you'll be okay.
Light and Ryuk have been known to hang out watching wrestling matches and playing video games in between plotting and executing bouts of mass murder.
In D.Gray-Man, when Tyki is invited over to the main villain's lair, he ends up having to help one of the Earl's favorites, Road Kamelot, with her homework.
The Noah family in general would be a normal, happy family, enjoying family dinners and helping each other out when they need it, if not for the whole "wanting to destroy the world/kill God" thing.
Tyki also has friends from before he awakened as a Noah. Whenever he's not being an evil henchman, odds are, he'll be with them. This was actually how he met Allen the first time.
Lord Il Palazzo, from Excel Saga, seems like the typical Evil Overlord. But when his operatives are out doing his bidding, he's left to his own devices. Plotting world conquest? No, just playing video games, learning guitar, reading comics, and teaching himself foreign languages.
Much of the manga is spent following Excel and Hyatt (and later Elgala) as they try to hold down a succession of low-paying jobs, trying to make ends meet.
Baptistin out buying French bread for the Count of Monte Cristo in Gankutsuou is quite memorable. The manga even includes an omake that shows him kneading bread with Bertuccio and launching into a tirade (complete with images of him throwing around breads and pastries to admirative crowds) about how he's going to become the best baker in Paris. The two-page omake then ends on the Count and his servants eating and decreeing that, really, Baptistin's bread isn't very good.
Organization XIII from the Kingdom Hearts: Chain of Memories manga do this: Zexion drinks tea and makes tsukemono (Japanese pickled vegetables), Lexaeus reads manga and solves puzzles, Vexen likes to complain about people not realizing/outright ignoring his seniority, Larxene reads Marquis de Sade, Axel reads books about cooking, and Marluxia and Larxene have dinner together.
In the 358/2 Days Manga, you also have Xaldin, Zexion, and Demyx playing Twister.
And the actual game of 358/2 Days shows us what Axel and Roxas like to do when they're off duty: hang out on the Twilight Town clocktower and eat ice cream, as shown in one of the previous page illustrations. In the same game, the other Organization members lounge in their castle's equivalent of a living room.
Several scenes with Hayate and the Wolkenritter in the first half of Magical Girl Lyrical Nanoha A's feature one or more of the antagonists hanging out with Suzuka, having a nice dinner at home, or out shopping, in a manner reminiscent of scenes featuring Nanoha's family and friends. This is in between or even during scenes where the Wolkenritter are beating the crap out of the heroes and stealing their Mana. All they want is to be a happy family, anyway.
Semi-used in Strikers. Shortly after the new cyborgs are activated, most are seen relaxing in baths, sipping tea, or, in Scaglietti's case, getting a trim from his secretary. The only one who doesn't relax is Sette. This serves to emphasize her position as the most robotic of the Numbers.
Arf is introduced relaxing at a hot springs while Fate looks for the Jewel Seed. She encounters Nanoha with her friends and, unimpressed with her, threatens to eat her if she gets involved. The next episode shows her having dog food for dinner before checking on Fate.
Mazinger Z: Several times, when the heroes infiltrated into one of the submarine fortress of Baron Ashura's, he/she was taking a relaxing shower (and he/she did not appreciate being interrupted. Nobody -including the heroes, Ashura's minions and the audience- did, in fact). And often he/she was shown playing organ or drinking a glass of fine wine in his/her private chambers.
Once his initial arc introducing him as a bad guy in Mythical Detective Loki Ragnarok is over, Heimdall spends nearly all of his time getting dragged out shopping by Frey.
While this is never directly referred to, the Big Bad in Noir is mostly seen in the beginning of the series picking grapes, writing letters, and taking walks in the sunshine. This has the effect of making her more creepy than the previous mafioso punks and thugs.
In Saint Seiya, the Sanctuary Pope aka Saga, the Gemini Gold Saint, was often shown either bathing or showering. Since he was a strong fighter with quite a nice body, this was used as Fanservicefor the female viewers. He wasn't the only one, though: in the anime-only Ansgard saga, the Brainwashed and Crazy Princess Hilda was often shown feeding her pet crows and tending to her small garden.
Later in the series we also have Hadesdragon Thanatos. Who is introduced when he is having a small concert for some nymphs.
In the second season of Slayers, while the party gets sidetracked from their main quest by the royal family, Zelgadis complains that Xellos will get ahead looking for the bible. Cut to Xellos enjoying a nice glass of water at a local cafe.
It was cake...or possibly steak. In the manga, it was definitely steak, not very cooked, and he was eating it with his arms still pinioned to his sides by his self-torture sarcophagus. And this was about where Midvalley decided it was embarrassing to be obeying this guy and tried a coup. No dice, partner.
In the anime, Legato is often seen in the background, calmly eating soup in a bar. At one such occasion, he witnesses some local thugs trying to molest a woman... and calmly mind-controls them to kill each other, continuing to finish his soup all the while and then leaving without saying a word.
In X/1999, when Seishirou and Fuuma are not out murdering people or destroying Tokyo, they enjoy eating ice cream and other not-so-evil things. Which drives home how much of a heartless bastard they can both be, saying things like, "What a pity, the ice cream shop will be gone because of our earthquake".
Pegasus from Yu-Gi-Oh! was once depicted eating dinner and reading a comic as the various duelists unwittingly aided his evil scheme. The comic's apparently the inspiration for Pegasus' nigh-unbeatable Toon World deck.
The third-party villain Tron from Yu-Gi-Oh! ZEXAL is seen watching cartoons in a few scenes. (Although in one of them, he's doing it while his henchman IV is nearby, negotiating with some mercenaries to deal with Yuma.) The villains Gilag and Alit are shown hanging out in a bar and Gilag gives Alit advice for his crush on Kotori. Gilag also watches TV (but he seems to steal cable) and reads manga frequently. He even draws some manga sketches and shows them to a manga artist, who says they suck.
On two occasions in Naruto, members of Akatsuki are seen having dumplings for lunch; once in the beginning of the Return of Itachi arc with Itachi and Kisame, and once in the Three-Tails Arc with Deidara and Tobi.
Envy from Fullmetal Alchemist was revealed in one of the video games to have a thing for...chocolate parfait. Yes, how fearsome.
While Gray and Gray Morality means that no one is clearly a villain, there are still plenty of Antagonist Out Shopping scenes in Darker Than Black. First, for the British agents- April visiting a host club and complaining when the hosts collapse from drunkenness after she out-drinks them. Her partner November 11 is shown to have a Funny Answering Machine, and is a fairly nice guy when off the job.
In the same episode, November 11 is kidnapped by Amber's henchman Maki, a Creepy Child, and Amagiri, who have just finished blowing up several embassy buildings. Maki spends his spare time learning Japanese and complains about burning his tongue from his Remuneration of drinking hot milk.
A later episode has Amagiri complaining about how his Remuneration of eating hard boiled eggs is bad for his cholesterol.
Then again, Claire is arguably the main, or at least most proactive, hero. Yeah. It's that kind of series.
In one of the light novels set in 2002, the leader of SAMPLE starts one of their cult meetings by apologizing for his lateness - he kept dying on the final boss. Those Japanese shooters are hard.
Tentai Senshi Sunred is made of this trope, featuring villains with crappy part time jobs, the head of the evil organization getting lost in a department store, and sentai monsters having domestic squabbles about who ate whose ramen, among other things. The ending theme is set to a heartwarming sequence of the evil organization having a family dinner around a cozily small table.
An example which overlaps with Go-Karting with Bowser- in an episode of Busou Renkin, the Affably Evil villain Papillon wants to meet and talk with the heroes at a neutral location, and they chose the local burger joint. The waitstaff are horrified by Papillon's signature stripperific butterfly outfit and try to subtly indicate that they'd prefer him to carry out. It gets even funnier when the Large HamBig Good Captain Bravo shows up in his costume and, like Papillon, is adamant about eating in the restaurant, and indicates his desire to eat there regularly.
In Tokyo Mew Mew, Taruto, Pai, and Kish are once shown eating parfaits while complaining about global warming.
A variation occurs in YuYu Hakusho, as demon hunter Sensui spares a demon, Itsuki, after the latter asks for one more day of life so he can see the finale of his favorite TV show. This small request catalyzes the change in Sensui's belief of demons being mindlessly evil threats to the belief that they are rather human - and sometimes better people than actual humans.
Kira Yoshikage, psychopath tendencies aside, was just your average wealthy businessman. He went to work, got his suit tailored, bought sandwiches,etc.
Pokémon features the Team Rocket trio in this trope semi-frequently. One episode had Giovanni spending time catching some rays at the beach while James and Jesse pestered Ash and co. while they were researching Slowpoke evolution.
Even though the rest of his crew is doing questionable things, in One Piece, we meet our likely final Big BadBlackbeard just having some cherry pie and ale in a random bar.
The cover stories after the war also show the Marines lounging around, most notably, Admiral Akainu cutting a bonsai.
The CP9 members actually go shopping during their Cover Story while they wait for Lucci to recover. After he does, they go bowling.
Cover-stories in general focus on defeated villains trying to deal with their lives after being clobbered by the Straw Hats. Wapol ends up forming a conglomerate, Hatchi fulfills his dream of owning a Takoyaki stand, and Gedatsu starts up his own hot-spring resort. The rest of the Baroque Works Officer Agents start up another Spiders Cafe.
The manga MegaMan Gigamix has some of the Robot Masters get part-time jobs at an amusement park. They dub themselves "The Part-Timer Squad" and consider their duties Serious Business; when they're on the clock, they see nothing wrong with helping MegaMan and ignoring Wily's orders, as making customers happy is more important to them.
Douglas Rosenberg, the Big Bad of El Cazador de la Bruja, spends much of the second half of the series on vacation, in order to avoid raising unwanted attention, but the casual comments he makes, like "fishing requires patience", imply that, at the same time, he's keeping a close eye on the protagonists.
The 4th Hellsing OVA ED features the Millennium Organisation destroying London completely...Then moving on to Japan, not to destroy it, but to become otakus. All this, while Schrödinger strolls happily in the foreground. While in no way canonical, it is absolutely hilarious to watch The Major, Captain, and Doktor amongst the other prominent members of the organisation walking around acting all nerdy.
In the episode proper, Rip's lieutenant laments that as a vampire he can no longer do simple things like feeding pigeons in the park.
Androids 16, 17, and 18 did this a lot. One scene even had 18 shopping for new clothes.
In the new movie, the God of Destruction Bills and his attendant Whis enjoy eating Sushi, playing bingo, and breakdancing before proceeding to fight the good guys.
Zigzagged during the Buu Saga in one scene with Majin Buu, who has achieved his Super Buu form. He gets bored with no-one around (the heroes are trying to figure out how to make a successful attack against him, and he's not only somewhat concerned about it), and decides to get a snack at a bakery, saying, "no sense destroying the world on an empty stomach". (Well, he doesn't pay for anything, but then, the bakery and the town itself is deserted due to the crisis.)
Revolutionary Girl Utena applies this trope to the student council members in the filler episodes, and to the point of eeriness with Akio near the end of the series.
When new villain, Villagiulio, appears in Rinne no Lagrange, he seems to be a serious deal. In the very next episode he spends most of time goofing out at the beach and goes drinking with Madoka's uncle after they got into a fight over a coat they both wanted to buy.
In Beelzebub, a side arc involves tissues from the demon world, which summon members of Behemoth's 34 Pillar Squad (En's personal army) when used properly. The arc just so happens to take place during the squad's monthly trip to a family restaurant, and they're all very annoyed that their meal-time bonding is being interrupted.
Done in an episode of Sailor Moon S. The villain actually comes back from shopping to find that he's locked out of his house. Cue him doing his Face Framed in Shadow/Large Ham moments in public and snacking on the food he bought.
There's quite a bit of this in the anime adaption of Valkyria Chronicles. You have Jaeger fooling around, Selvaria trying desperately to do whatever Maximillian wants done and Karl hanging around trying to be helpful. Neither Gregor nor Maximillian take part in this, which is a clue to who the viewers are supposed to sympathise with. The OV As play this up even further. The first two end with Selvaria hanging around a beach alone, and hanging around at a fesitval alone, hoping Maximillian will turn up. Then there's Selvaria's dress-up OVA and the card-game between the four main villains.
Ratman is centered around an evil organization that does this on a weekly basis. They're less about world domination and more about causing chaos, just to discuss it over Fatman(CO) pizza. Most of the plot arcs involve abnormal heroes noticing the fully-dressed minions (Jackies) shopping around for daikon. Normal heroes don't think they exist because of the ridiculously low bounty (FIVE. HUNDRED. YEN.), but weirdoes attracted include a catgirl with wrestling mastery and a maid android with rocket arms.