Mundane Side

Almost any fantastic premise (with very few very, very strange exceptions) has to implicitly or explicitly rely on many non-fantastic elements -- and those usually provide the easiest starting points for exploration, deconstruction or humour.

Often, if you think things through, fantastical elements themselves may involve less fantastic things either as requirements or results of their presence. Sometimes there are Required Secondary Powers or refueling with Unobtanium. There are inherent limitations such as Exact Words or outstanding power corrupting outstandingly. But even more often, there are implicit familiar, or at least down-to-earth sides: after all, someone would have to make and repair saddles and all the other tackle for your Dragon Riders. Which is an extension of the classical Sci-Fi/Fantasy approach — after all, The "Unicorn In The Garden" Rule works because the authors have their hands full handling consequences of only one fantastic element.

Conversely, one can start with something mundane and downright trite, and refresh it by exploring how it could function in a fantastic setting.

Both variants can be exploited a source of comedy, drama or plot-limiting rules... or as filler. Overlaps with Bathos. See also Mundanization for an episode in the "mundane" part.

Generic

 * The Hatless in the Land of Hats. Explore how a Planet of Hats needs people not wearing the hat (or at least willing to remove it for a while) to remain competitive - and often to survive at all. Yet Klingon Scientists Get No Respect. Or maybe some of them receive great respect, but all the fame among the outsiders goes to the more visible people?
 * Variations on the Extranormal Institute or All-Ghouls School.
 * Treatment of fantastical objects as the equivalents of common objects, justified or not, allows both gag and serious use.
 * E.g. treating the Crystal Ball as a computer (so it sometimes hangs and have to be rebooted, freezes in the limbo of "...waiting for connection..." and so on).
 * Familiars. Several cartoons (including a few in Dragon) dealt with the question of how one get the familiar to a veterinarian.
 * Stock jokes like "My other steed"/"My other spaceship"/etc is… and endless variations of "Kick Me" Prank.
 * Recycle the Freudian Couch. It provides a simple and nearly universal setup for this sort of humor (and also horrible puns, should the author be so inclined).
 * Dragon had cartoon with a dwarf complaining that he "suffers from low elf-esteem".

Literature

 * Wizarding Britain in Harry Potter does not appear to have any Wizarding agriculture -- every magical family we hear about is either aristocracy or has breadwinners in white collar jobs (Ministry workers, journalists, shopkeepers, and so on). More than a few fan authors have pointed out that just to maintain subsistence levels they would need to import a fair amount of food from Muggle sources (and probably other goods as well).

Tabletop Games

 * Generally, often used to improve atmosphere.
 * There are various extras like "List of 101 Fantasy Professions", treating it as a niche into which to spread.

Web Comics

 * Eerie Cuties started with an All-Ghouls School, but didn't stop here. If there are enough of teen vampires, of course there should be... the Teen Vampire Magazine.
 * Seen again in Magick Chicks, here.
 * Evil Inc. has a lot of this stuff from the very premise.
 * Also, the classics - one crystal ball that required a "reboot" from the witch (but ).
 * Chuckle-A-Duck has "good dog" on a Freudian Couch.
 * Sword Comic has [//swordscomic.com/swords/CCLXXV/ a page] on talking swords and — two things that don't go well together.

Web Original
"What would Iron Man do if he was a common man struggling with everyday travel and issues?"
 * GlennZ uses both sides of this.
 * Just in one set: Banana gun — reloading and mounting Laser Sight. What happens after you use a Hover Board? You plug it into a recharging station, of course! See also: a stick insect taking selfie.
 * Iron Man Grounded Project. See also a sample on Behance) by Raffael Dickreuter.

"alien crime lord> in the mornings, I slither out of bed and choose which skeleton to wear. sapphire or silver? solid or hollow?"
 * [//twitter.com/ctrlcreep/status/690608365165158400 This] Twitter micro-fiction, on some decisions amorphs have to make: