The Astro City story "On the Sidelines" is centered on this trope — it's about a group of super-powered beings who use their abilities in everyday life, with no interest in being superheroes or villains. Examples include a telekinetic who controls things for stunt work, a fire-manipulator who's a glassblower, an empath who's a club deejay, and a man with Super Strength who works in construction. Then a super-villain comes along who thinks their lack of world-breaking ambition make them ripe for exploitation...
Bamse's super-ursine strength is probably more often used to help people with mundane tasks (the ur-example comes from the very first comic, where a kid lost some money under a truck, and Bamse casually moved it). At least for a while his day-to-day job was lumberjack, where superstrength comes in handy.
In Dark Times, former Jedi Master Kai Hudorra uses his force powers to earn a small fortune as a gambler, then set up a casino. As a Jedi living during The Purge, he has good reason to not use it in any flashier way.
Clara of Death Vigil can draw magical portals in the air which can cause a monster charging at her to suddenly find itself a hundred meters in the air and falling to its destruction. Or, she can use them to scratch her own back.
Empowered: One advantage of shacking up with a girl with a super-strength granting alien battlesuit? Darned easy to rotate the tires on your SUV. It's also been shown once that, since she can't carry tissues (no pockets), she has to wipe her "tears and snot" away with her hands and then "mini-vorpp" them dry.
Ex Machina gets a lot of use out of this. As the main character is a retired superhero who isn't legally allowed to fight crime any more, he's as likely to use his Technopathy to change TV channels as to defend himself.
Groo the Wanderer once used his sword to cut a pear from a tree. Not much of a mundane utility in itself, but it was worth it to see how his dog Rufferto chased after him, expecting a vicious battle, only to be disappointed by the outcome.
In one early issue Groo is asked to demonstrate his swordsmanship while he's face-deep in a seafood feast. In the time it takes to finish the question, he draws his sword, coats it with brandy by slashing through a bottle, flips one of the fish into the air, slices it into six fish-steaks, kebabs all six on the point of his blade, and thrusts the brandy-soaked fish slices through a nearby torch to set them all aflame. He then slides the still-smoking fish fragments onto the king's plate with his other sword.
Advisor: Did you not see that, Your Majesty? Are you not impressed?!
Livewire of Harbinger is a technopath who can text and tweet at once. She's used this skill to save her team before, albeit a different one.
Hellboy's Liz Sherman uses her pyrokinesis to light her cigarettes on occasion.
The Plutonian in Irredeemable is seen using heat vision to warm up a cup of coffee.
Lori Lovecraft: After her apartment is trashed by an earthquake in Into the Past, Lori uses her spare crystal ball to watch the basketball game she had been taping.
In Mega Man (Archie Comics), the second issue's Short Circuits had Cut Man being used as a ribbon cutter, hedge trimmer, and to give Dr. Wily's hair a trim. Needless to say, he's unhappy.
Another issue had Quake Woman, Centaur Man, Elec Man, and—surprisingly—Time Man using their abilities to save lives during a global blackout.note Respectively: drilling holes in doors/walls to let trapped people escape, running through floodwaters to rescue people from drowning, acting as a generator, and using Time Slow to assist in surgery.
One Mighty Morphin' Power Rangers comic had Kimberly use her Power Morpher as a cup coaster. It bit her in the butt when she forgot it and she was needed.
The title character of The Pro uses her Super Speed to give 1,000 blowjobs in a single night.
Well Spoken Sonic Lightning Flash of the Super Young Team has been known to use his super speed to tear up the dance floor.
Sara Pezzini has used her Witchblade, a cosmic artifact of nigh limitless power, to move furniture while moving, make toys for her daughter and to hold up her towel while she answered the phone.