Doctor Horrible's Sing-Along Blog is this trope like red is a color. When he isn't building freeze rays (Stops time. Tell your friends.), Billy (AKA the titular Doctor) is doing laundry, checking mail, and trying to work up the courage to confess his feelings toward an ordinary girl named Penny.
The only formal interview Lord Doom, the primary Big Bad of the Global Guardians PBEM Universe, ever gave to any member of the press was to a seventeen year old high school girl who asked nicely in an open letter posted to the internet. The inquiry intrigued the master villain, and the girl got international fame (and a very, very interesting story for her school newspaper) when he agreed to her request. While the interview started off as the standard piece, it eventually descended into a three-page discussion about classic rock music, James Bond films, favorite books, and where one could find the best pizza on the planet.
Later installments of the series feature Villains and Heroes Out Shopping (or drinking, anyway), as they focus on both sides relaxing, unwinding, and shooting the breeze at their local drinking holes. In typical fashion, the hero bar is a rather calm, sedate place where water costs $4.99 because most superheroes don't drink booze (except, notably, Iron Man), whereas the villain's hangout is generally a bit more raucous.
Taken even further by the "Goblin Bloggin'" segments by the same author, in which Green Goblin hosts a YouTube vid-blog, and generally furthers the impression, gained over the previous 'Marvel / DC' installments, of being quite an Affably EvilAnti-Villain with a deluded crush on Harley Quinn in this universe (albeit one with a psychopathic hair-trigger temper, an almighty grudge against Tony Stark, and a slightly uncomfortable obsession with Willem Dafoe).
This delightful gem from Kajet begins with Castlevania Big Bad Dracula enjoying some delicious pot roast...when he is informed of a Belmont in the castle (PFFFT). (Caution, lots of cursing)
Marik Plays Bloodlines is a miniseries of this, spinning off from Yu-Gi-Oh! The Abridged Series. Yugi's mortal (if rather kooky) enemy is apparently taking time off at some unspecified point to LP Vampire: The Masquerade, complete with fellow villain Bakura snarking at him in the background.
SCP-1295 from the SCP Foundation features the Four Horsemen of the Apocalypse. Due to a screwup on the part of War, who mistook the detonation of an atomic bomb as the beginning of Armageddon the four old men are stranded on Earth. In the present they spend their days patronizing a diner, and only manifest dangerous powers if anything or anyone tries to keep them away from it. The four enjoy the diner's food, coffee, and atmosphere while counting down the days until the world truly ends.
The Spoony Experiment features a Mad Scientist villain named Dr. Insano, who plots to take over the world ''with science''. Despite claiming to have killed thousands with his army of robotic suicide squirrels, and winning the 2008 presidential election, what we mostly see him doing is sitting around Spoony's house, helping with reviews (and occasionally doing his own), and fixing an Atari Jaguar CD.
In Survival of the Fittest, Danya, when not kidnapping hundreds of high school students at a time and forcing them to fight to the death, is shown to enjoy spending quality time with his loving wife and adorable eight-year-old daughter.
For most of Vaguely Recalling JoJo, DIO is out having a vacation with Giorno, and frequently runs into Jotaro and the others, as a result.
A Very Potter Musical has Voldemort arguing with Quirrell about laundry in his first scene. Later in the show, they go out and get drunk, talk about watching She's All That, and rollerskate.
Newsreader: Voldemort blogs about [his return to power] on his new FlooTube channel.
Voldemort: I'M GONNA FIND HARRY POTTER AND I'M GONNA [bleep] IN HIS [bleep]!
Voldemort: Well, it was a little slow at the beginning, but come on: Zac Efron! Zefron! 'Nuff said.
Obligatory Whateley Universe example: In the Bad Seeds' Christmas story, the Seeds (all children of supervillains), when they aren't trying to steal energy from Seraphim or beat up the supervillain leaving She-Beast's real name on crime scenes, are using their time in New York City to shop. Legal shopping for Christmas gifts. Except Sociopathic Hero Jobe, who is using his downtime to do biological research and argue over the phone with other researchers, which turns out to be an enormous Chekhov's Gun.
In Worm, the main character spends some time alternating between her role as a supervillain and being a troubled teenage girl, taking runs and even shopping on occasion.