In Star Wars: Knights of the Old Republic, the player can often find him or herself in situations where Sith soldiers or even Dark Jedi are "off duty" in a lounge, bar, or simply keeping to themselves. This is the entire point of the world of Manaan, where a neutrality treaty has forced enemies to work in close proximity to each other without fighting. The player can even accept sidequests from some of these characters to help them out.
The sequel has a rather hilarious conversation tucked into Dantooine, where the player confronts one of the mercenaries plaguing the planet, while he's placidly (and helpfully) spelunking. As he says, even professional killers need hobbies.
The Pigmask Army from MOTHER 3 may be soldiers of an evil regime, but they sure love rock concerts!
Lucas and his party also encounter some pigmasks who are in the middle of a discussion about whether they hang up their masks when they use the bathroom.
Before one battle with the Turks in Final Fantasy VII, Cloud and his pals listen in on their conversation about who they all have crushes on.
If you immediately went to Costa Del Sol after getting off the cargo ship, you can catch Hojo chilling on the beach, being attended to by women.
This may actually be one of the very few instances where a Complete Monster falls under this trope. At this point we don't know really know about most of his horrible crimes against nature.
The Wutai sidequest has the Turks invoking this trope, by having Rude and Reno remind Elena that they're on holiday (no really) when she tries to fight the protagonists. At the end of the quest after you've rescued both Yuffie and Elena, they decide that they're "still on holiday" when they get a call from their boss telling them to catch Cloud.
Except for Xemnas and Saix, all the members of Organization XIII are shown to be pretty relaxed outside of their missions in Kingdom Hearts: 358/2 Days. The good guys among them, Axel, Roxas, and Xion, make it a pattern to go eat ice cream atop Twilight Town's clock tower after each mission is accomplished.
In the manga, you even have Marluxia and Larxene drinking soda pop (XIII Squash) and eating KFC.
And also in 358/2 Days, it's mentioned that they have a poker league. Seriously.
In general, The World That Never Was, which was a Very Definitely Final Dungeon in Kingdom Hearts II, is made to feel more like a place where the Organization members live between missions. They even have a break room.
Persona 4 examples, though their true natures are unknown until far later in the game. You can find Namatame on the streets. He will talk about how he got a new job recently and is trying to recover from the reporter he loved dying. Adachi also shows up on some days in Junes. He likes to buy cabbage.
And then there's that gas station attendant that likes to make small talk with you and only works when it rains...
In the "Heaven's Feel" scenario of Fate/stay night, Shirou ends up having a rather cordial conversation with a major villain of the two other arcs in a Chinese restaurant while the other is busy eating mapo doufu. While the character has been mostly personable so far in the arc (and asks the protagonist if he wants some of his doufu), knowing what he is capable of in the other two scenarios makes this a major example of this trope.
It's never certain if Kirei isn't trying to kill Shirou through the doufu.
This is the point of the "fun disk" Hollow Ataraxia, where every antagonist and protagonist are shown just trying to have a normal life in Fuyuki City. Including Caster's cosplay hobby, Caster sweeping up staircases by herself because she doesn't believe in wasting mana, Lancer attempting to hold down a job as a grocery boy, and the main antagonists Gilgamesh and Archer getting into a fishing contest because they both wanted to annoy Lancer after he insulted them while fishing. Also, football. And arguments over food. Everyone in Fate/stay night show up except for Kotomine (who is dead and therefore not causing any trouble. Because he's dead.), because he would attempt to be villainous even in these circumstances.
And Tsukihime has an extremely bizarre conversation during Kohaku's route, between Shiki and one personality of the game's Big Bad, on a downtown sidewalk, as the two drink coffee and have a cordial chat on how society judges murderers like them. It's notably the only path where Shiki doesn't fight — or even make an enemy of — either of the Big Bad's personalities, due to that little chat and its end result of the Big Bad recognizing Shiki as "the better killer".
In the superhero MMORPG City of Heroes, instead of wandering monsters, you'll find groups of mooks standing around committing crimes like breaking and entering or purse-snatching...or sometimes you'll just find them standing around having Seinfeldian Conversations. Though they'll still attack your hero on sight...
World of Warcraft has several occasions where you can overhear enemy mooks chatting about very mundane things. Examples include a blood elf mob (in Quel'Danas) wanting to get a house by the sea when the war is over, a human guard (in "Escape From Durnholde") chatting about his/her coming vacation, and the members of a demon-worshipping cult (in Terokkar) who talk about playing leatherball, going to a nearby town for some drinks, and having difficulties controlling an Eldritch Abomination they summoned. Oh, and you usually end up killing all of them.
Rival player territories can also have a similar effect. The first time you travel to the territory of the opposing faction, it feels like a dangerous mission deep behind the frontlines where only unknowns exist and the enemy lives in their wholly alien ways. Cue sneaking into Stormwind and finding level 1's running about and naked players dancing on mailboxes. Just like Orgrimmar. Or finding players who use emotes to break the language barrier.
It's also worth noting that in the prior game, Mario & Luigi: Partners in Time, Fawful was a shopkeeper who exchanged beans for badges. Only Baby Mario and Luigi met him though, and he doesn't recognize them.
Dr. Nefarious: Aaaand... action! You'll never take me alive, Qwark! Time is under my control!
Lawrence: ...Oh, am I interrupting?
Dr. Nefarious:Lawrence! I'm rehearsing my epic romantic action comedy space opera!
Also, near the end of Up Your Arsenal we learn that Lawrence himself plays bass in a rock band. And when we learn this it's almost time for his solo.
All of the Myst villains describe aspects of their lives in their journals. Sirrus writes about gardening and exploring Spire, Achenar writes about the local wildlife and the construction of his various outposts, Gehn writes about finding frogs for his pipe, and Saavedro writes about making plant hybirds. It helps humanize them as well as inform you about their antagonistic deeds.
Commonly found in the Streets of Rage series. Female mooks are enjoying the night life at a club when you bust in to beat them up, and several mooks can be found sleeping on benches, eating, or brushing their hair before they spot you.
At one point in the second game, you jump into the back of a parked truck. Several biker mooks are gathered there, and you prepare for a fight... wait, you can't hit them? Then you spot a miniboss, and see they're pumping their arms. These guys are the audience for an underground fighting ring. (They won't attack until you defeat the current champ.)
There's a superb, but all too brief, one of these in a high-speed chase in the ice level of MDK - at one point, the hero and his pursuers, busy in a firefight whilst iceboarding, crash right through a small guardhouse - which contains a mook sitting in an armchair, reading a paper, who gets briefly swept along with the rest of the fight for a few seconds (continuing to obliviously read the news) before being obliterated in the hail of bullets.
In the French RPG Off, we see The Batter have fun on a roller coaster and get his photo taken.
In Darkstalkers, Baby Bonnie Hood has a ten-part routine; nine of the ten parts are activities that would seem typical for her role as a deceptive and heartless Professional Killer, such as training in marksmanship, maintaining weapons, and researching marks. (Plus some rather unethical ones, like gaining weapons by stealing them, so as to be untraceable.) Number 5 on the list, however, is innocent enough: "5. Going to town to buy food and clothing, and going to Grandmother's house to do errands."
The protagonist can also be this: You may be an psychotic murderer or master thief, but doesn't mean you have to visit your local vendor to resupply and/or pawn all your stolen loot, and heck, you may even help the area out a bit when you got a second to listen.
In The World Ends with You, Reapers are allowed to phase into the mortal plane and lead relatively normal lives when they're off the clock. 777, for instance, spends his spare time as part of an indie rock band.