DC's Justice League. Things can get serious for the Man Of Steel in the comics, too, but much of his four-color past has involved some very silly and funny storylines.
From the goofy stories of the Silver Age, when continuity or logic didn't always factor as much as they do now, to the extreme era of the '90s, Superman has been involved in some zany stories. There are many comic book stories that could inspire the next Superman movie, but likely none of these somewhat ridiculous ones.
Lois Marries Super Baby
In Superman's Girl Friend, Lois Lane #57 from May 1965, Lois Lane marries a baby Superman from a different dimension. It's exactly the kind of nonsense story that this period of Superman was known for. The story saw Lois competing with Lana Lang, Clark Kent's love interest from Smallville, for the affections of the young Man Of Steel.
The real Superman was more or less just hanging out and watching the entire episode transpire, but like many stories of this period, it was presented as only a 'possibility.'
Burning The Bat-Witch
Superman is in some ways an unlikely friend of Batman, given how different they are. But they're traditionally close friends and allies, which is why the comics had so much fun depicting them as adversaries. A famous and fun example occurred in World's Finest #186 in 1969.
This story had Batman and Superman flung back in time to the American Revolution. Batman is accused of being a witch and locked up in the stockade, which occurred only partly because the two superheroes had turned on each other a little.
The Feud Between Batman And Superman
Depicting Batman and Superman as adversaries was a mixed bag on the big screen but another issue of World's Finest has them duking it out. The two fight in a gladiatorial match in issue #143 of the series (later reprinted in #170), which stems from a scenario where Batman is inadvertently hit by a ricocheting bullet that bounces off of Superman's skin.
With some very complex intervention from the mayor of Kandor, the two friends find themselves locked in battle.
Red Kryptonite Superman
The mythology surrounding kryptonite was very loose early on, which led to the introduction of red kryptonite. Red kryptonite differed from the original green substance in how it affected Superman depending on continuity. Mostly it gives him strange and unusual powers.
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In Action Comics #283, it even caused Superman to breathe fire. The humor in the story comes from Superman breathing dragon fire any time he speaks, so he uses another power he never had before, ventriloquism, to speak to his friends.
Distant Fires
A more modern story that was inadvertently funny was Distant Fires. This Elseworlds story from 1998 was written by Howard Chaykin and drawn by legendary comic book artist Gil Kane. In the story, Superman is said to be the last survivor of a nuclear holocaust. The gloomy tone is offset by scenes of him fighting giant rats while riding on the back of a giant cat.
He then eventually discovers some survivors, including Wonder Woman, whom he falls in love with (something that happens a fair amount in DC Comics). His peace is destroyed again when Shazam, who's jealous of him, destroys the world a second time.
The Red Superman
The Elseworlds concept within DC Comics is really an outgrowth of stories in the '50s and '60s that were essentially all 'what-if' tales (which Marvel will investigate in the What If..? Disney+ series). One of these stories has Superman splitting himself into two versions, one red and one blue, to try and keep up with all the heroics he has to do.
This story appeared in Superman #162 in 1963, and would in a roundabout way inspire the "Electric Superman" from the 1990s. This also split Kal-El into two clones, one red and one blue, in another fun and crazy story.
Jimmy Olsen Marries A Gorilla
The tone of the earlier Superman comics was generally all over the place. One of the wackiest stories occurred in Superman's Pal Jimmy Olsen #98 in 1966. Jimmy Olsen very nearly marries a gorilla in the story, which hasn't aged well on many fronts.
The funniest thing, or the most concerning perhaps, is that Superman officiates the ceremony. Jimmy Olsen has suffered a little bit in the comics and in the movies, even dying unceremoniously in the director's cut of Batman v Superman: Dawn Of Justice.
At Earth's End
The '90s were an extreme era in comics in general, and no superhero was immune. Superman played a major role in setting off the '90s comic speculator boom with The Death Of Superman, but it was another story that is perhaps more emblematic of the era. In At Earth's End, an older Superman loads up with the biggest gun possible.
This is another ostensibly serious story that takes place after another nuclear war, but the end result is something unintentionally funny. The image of an older Superman with such an outrageous weapon is memorable for all the wrong reasons.
Super-Menace
Zack Snyder's Justice League teased the idea of an evil Superman, under the thrall of Darkseid. There have been 'evil' versions of Superman in the comics. One of the most fun was the Super-Menace.
This story suggested Kal-El had a twin in the escape pod with him when he landed in Kansas, who would grow up to become Super-Menace. This happens in Superman #137, where a pair of criminals find the previously never before mentioned (and never mentioned again after) twin.
Making A Movie With Big Barda
One of the strangest and most inadvertently comic stories involving Superman also concerns Big Barda, the wife of Mister Miracle. The two are manipulated into making an adult movie by a supervillain named Sleaze in Action Comics #593.
Mister Miracle intervenes before things get too out of hand and Sleaze can use the intended video as a weapon against the Justice League. The story is courtesy of John Byrne, who was also writing some very humorous and fourth-wall-breaking stories in She-Hulk around the same time.