While being one of the most horrible villains in the DC universe, Darkseid has also done some surprisingly normal things, like work at a Burger Fool, buy Earth porn and later watch it (purely for "research" purposes, and to force his adopted son Scott Free to watch it [if only because Scott's wife was in it]), and was once even mugged, and spent most of the time just analyzing the experience.
In the final volume of The Sandman, we see him attend a funeral. Admittedly, it was a funeral for the King of Dreams and took place in the Dreaming, but he was still just sitting in the pew and listening to the eulogy like anyone else.
In the 9th issue of Judd Winick's Outsiders, the demon Sabbac inflicts third degree burns on resident tank Grace. The scene cuts away after a strategic retreat by the eponymous team, and when next Sabbac is shown, he's trying on a new suit. This is partly subverted in that he's murdered everyone working at the shop in incredibly gruesome manners.
Marvel Comics has the Bar With No Name, an establishment that caters specifically to super-villains. The Bar's first appearance did not fit this trope (it was where the mass-murder of several villains occurred during the original "Scourge of the Underworld" storyline in ''Captain America") but since then, the Bar has appeared in many stand-alone stories where groups of villains gather to drink and talk (or commiserate).
In the J. Michael Straczynski run of Spider-Man, Morlun, a villain who absorbs life energy, is out for Spidey. The hero and a mentor wonder what he's plotting and what evil rituals he's performing to prepare himself, cut to...Morlun trying out evil leather pants, and wondering whether they make his butt look big.
Another Spider-Man example is in Marvel's Webspinners: Tales of Spider-Man # 1, where Peter goes into a movie theater to catch a screening of an old sci-fi flick, and ends up sitting next to Quentin Beck - aka Spidey's foe Mysterio. Beck doesn't know who Peter is, and Peter doesn't recognize Beck in the dark, so the two foes wind up chatting back and forth about their mutual appreciation for film.
One Amazing Spider-Man comic that takes place during Todd McFarlane's run has the Chameleon reminiscing about the past while watching old Lon Chaney flicks on videotape. (He claimed to have been inspired by that actor.)
During the "Identity Crisis" storyline, Spidey spies on the criminal enforcers Roughhouse and Bloodscream; the former remarks how he's looking forward to the new episode of South Park.
In Superior Spider-Man, the first thing Massacre does after escaping from prison is go to a fast food restaurant.
In Thunderbolts, Atlas hangs out at a sports bar and discovers Man-Killer, a psychotically misandrist criminal, laying low by tending bar there. In this case, however, he, having been there before as a former criminal himself, manages to strike up a small friendship with her.
Done occasionally with the Nomad in Beau Peep, although the Legion were aware he was an Ineffectual Sympathetic Villain, they were less sure about his alter ego, the Desert Shadow.
Sgt Bidet: He's out there somewhere, Peep. A ruthless, bloodthirsty killer. (Cut to the Nomad under a palm tree with a bag of sweets) Nomad: Oh goody, nothing but red ones left!
Stilt-Man's funeral in Punisher War Journal is made of this. The Rhino angrily demands to be let in before quietly suggesting that the establishment should be handicapped-accessible, the Eel good-naturedly tries to keep Dragon Man from freaking out, etc.
In one issue of Uncanny X-Men back in the 1990s, Wolverine, Nightcrawler, and Colossus are out at a bar. The Juggernaut also happened to be there, just out for a drink and to try and pick up chicks. Peter had just broken up with Kitty Pryde, and Wolvie wanted to teach him a lesson. Cue Wolverine causing Colossus and Juggernaut to get into a Bar Brawl. That destroyed the bar. Juggernaut won. He then paid for the damage.
Another example occurred when members of the X-Men came across Juggernaut in New York City, where he was nefariously... opening a bank account. The time-traveling uber-sentinel Nimrod showed up and attacked the lot of them.
There's also the time during Grant Morrison's run on New X-Men when Wolverine and Sabretooth happened to run into each other in a bar restroom.
In the first issue of Doctor Doom and the Masters of Evil, the Sinister Six, Spider-Man's main group of villains, casually travel throughout New York, their appearances disguised by Mysterio's illusions. Amongst their daily activities are riding on the bus and buying hot dogs. Downplayed a lot as they do commit some villainy by using Mysterio's illusions to trick the guards of an armored car to give them their cargo, but they maintain their rather friendly banter while doing so.
The first arc of Gotham City Sirens, starring Poison Ivy, Harley Quinn, andCatwoman, starts not when any of the three launch an Evil Scheme to conquer the world or blow up a factory, but rather when they are attacked after Hush spots Harley when she is out shopping (And she is even paying for her purchases).
Subverted in one Empowered story. We see a group of ninja hacking a body into 100 pieces (per the client's request) whilst one ninja is monitoring and idly browsing the web in the next room.
In Godland, villains Friedrich Nickelhead and Basil Cronus spend their time together making normal idle chatter, for instance: discussing Field of Dreams and the appropriate emotional response to the ending. For the record, Nickelhead feels it was a cheap attempt at emotional manipulation, while Cronus holds that it takes a heart of ice to not be moved by it. A flashback shows master villain the Tormentor grumbling about his screenplay being subjected to Executive Meddling and deciding to inflict "the cruelest of all tortures — legal action" on the studio.
Happened regularly with The Tick; both heroes and villains, no matter how terrible or larger than life, ended up doing a lot of mundane stuff. In fact, the more terrible or larger than life they were, the more likely you were to see them at a convenience store or something similar. The ninjas had regular part time jobs.
In the second issue of Mega Man, the Short Circuits shows Wily lounging by the pool and getting his hair cut, all the while using Cut Man for Mundane Utilities.
While Namor's villain status is in more or less continual dispute, this does occasionally happen. At one point, he's seen surrounded by tanks protesting that he can't surrender, he's not here to invade... he just wants a bagel.
During one story arc of The Flash when Wally gave up his identity and memories of ever being the Flash, he had a chance meeting with Captain Cold when he had a late meal after his night shift at the police lab. Captain Cold was just having coffee at the diner. Cold was prepared to freeze Wally but relented when he realized Wally didn't remember him or even remember being Flash. The two former foes had a friendly chat and settled into a routine of meeting each other for food and coffee at the diner every night. The routine ended after Wally got his powers and memories back.
In the post-New 52 run with Barry Allen, the aforementioned speedster was looking for a job in downtown Keystone, and finds Cold drinking in a bar Barry was applying for a job at. The situation being reversed from the above (Barry knew Captain Cold, but Cold didn't know Barry's identity), Barry helped mix a drink Cold could imbibe without it freezing in his hand (due to recently obtained ice powers).
The Punisher doesn't spend all of his time killing criminals and getting into fights with superheroes who have a problem with it. He's occasionally shown going out for drinks and burgers.
Gargoyles: The comics continuation had Xanatos sending 2 drones, Coldsteel and Coyote 5.0 to get the powerful Stone of Destiny from Hudson, Lexington, King Arthur, Macbeth, and the local clan. They wonder what nefarious scheme Xanatos is really up to, and he's buying shoes with his wife. However at the end of the arc he uses the shoe box as a bomb scare and makes off with the stone. It's all pointless however.
Transformers: Robots In Disguise: With the war over, tensions rise to see who will restart it. Instead of scheming, some Decepticons just want to hang out at the (Autobot run) bar, and knock back a few drinks. Squawkbox and Tankor even decide to abandon the cause, because being at peace is better than going out to die over some half-remembered ideology.
Averted by The Joker at The laugh after Midnight at The Batman Adventures annual # 1, when after surviving his last fight with Batman only wants to come back home, buy some donuts and a paper, call to Harley to pick him... while killing the vendors with Joker Venom, offing a policeman (while stealing his squad car). The issue ends with Joker wishing he were home already... and idly wondering whose home it might be.