Superman and Wonder Woman are not only two of DC's most recognizable characters, they're two of the most powerful. It's only natural, then, for readers to imagine what a relationship between the two would look like. Just because they're the strongest man and woman in the DC Universe though, doesn't mean they make a good couple. Unfortunately, this hasn't stopped DC from attempting to push them together. Fans might recognize the handful of alternate universes and bad futures that depict Clark and Diana as some sort of couple, but that only scratches the surface.
Pre-Crisis
The duo's first romantic tryst, ironically, comes from Superman's Girlfriend: Lois Lane #136 in 1974. That saw Superman declare his love for Wonder Woman and passionately kiss her. As was common for the era, the attention-grabbing concept was deceptive, as the whole relationship is revealed to be a ruse to save Lois from a villain. The concept of a relationship would then be revisited in 1981's DC Comics Presents #32 where the love god Eros tricks the two into briefly dating.
The first time a relationship between Diana and Clark would be teased in one of their solo books would be the landmark Wonder Woman #300 which focuses on Diana's dreams. One dream sees Clark falling on to Paradise Island instead of Steve Trevor. This leads to an in-costume wedding where a priest comically refers to them as "Superman and Wonder Wife." Romance would be hinted one last time before Crisis On Infinite Earths completely rewrote DC continuity in Alan Moore's iconic story For The Man Who Has Everything. Wonder Woman gives Superman a single kiss for his birthday, which prompts Superman to ask her why they don't kiss more often.
Post-Crisis
Though DC seemed keen on pushing Clark and Diana together, the beginning and end of their post Crisis On Infinite Earths relationship would come in 1988's Action Comics #600. The comic sees Superman admit to loving Diana since they first met. He even goes as far as saying that he's had intense dreams about Diana. Though she does admit to sharing Clark's feelings, and the two do kiss in Earth's orbit, they both ultimately decide that they're better off as friends while Diana finds her place in the world. There is an implication that they might end up together in the future, but this plotline is completely dropped.
Kingdom Come
1996's Kingdom Come is one of DC's many dystopian futures. This one sees an older Superman fighting back against a wave of violent anti-heroes who have no problem killing supervillains. This eventually results in an all-out war between superheroes, ending with Superman fighting Shazam, and a nuclear warhead exploding that ends up killing most of the superhero community. The groundbreaking miniseries ends with Superman taking up his father's work as a farmer and accepting a pair of glasses, and a kiss, from Wonder Woman before she leaves for Paradise Island.
While that exchange might seem downright platonic compared to some of the previous relationships they've had, it is revealed in the sequel series The Kingdom that Clark and Diana eventually married and had a son named Jonathan, which makes this the first appearance of Jonathan Kent decades before he entered the main continuity.
The Dark Knight Strikes Again
While Wonder Woman is oddly absent from the original Dark Knight Returns, she plays a much more prominent role in its much-maligned sequel, The Dark Knight Strikes Again. This dystopian future makes it clear that while Superman and Wonder Woman aren't exactly a couple, they have slept together multiple times. Superman eventually takes up the task of mentoring their daughter Lara. Her unique heritage as both an Amazonian and Kryptonian makes her an incredibly powerful individual. Unfortunately, Diana and Clark have a decidedly antagonistic relationship as this version of Wonder Woman generally hates men.
Other Alternate Universes
Those might be the most well-known examples of alternate universes where the two have a romantic relationship, but they are far from the only ones. 1998's Superman: Distant Fires was a post-apocalyptic story where all of the normal humans are killed in a nuclear war and all of the superheroes are stripped of their power. Superman enters a love triangle between him, Wonder Woman, and Shazam. Shazam and Superman fight and Superman wins. After Diana chooses Clark over Billy, he rebels. Superman and Wonder Woman eventually have a son, Bruce, and everyone regains their power, leading to war which causes another apocalypse. In an echo of Superman's own origin, Clark and Diana send their son out in a rocket, away from the dying earth.
In a similar vein is JLA: Act of God from 2001. Through some method that's never explained, all of the world's heroes are completely stripped of their powers. This drives Clark into a depressive drunken spiral which ends with Lois Lane leaving him. He and Diana end up together, and the comic ends with their newborn child exhibiting some of the powers that his parents lost. There are also hints of a relationship in universes such as Superman: Red Son and DC: The New Frontier, though readers aren't given anything as explicit as what came before.
The New 52
It would take the entire universe breaking and coming back together again for Diana and Clark to fall for each other in mainstream DC continuity again. 2012's Justice League #12 made headlines with its shocking cover depicting Superman and Wonder Woman kissing each other mid-flight. They would eventually break up due to a combination of Superman's unresolved feelings for Lois Lane and other comic-related shenanigans. DC must have recognized how controversial this relationship was, as it was completely undone and erased from continuity by the time of DC: Rebirth.
Though writers seem to have fallen in love with the idea, it is far less popular with fans. Unlike some heroes such as Captain America or Batman, both Wonder Woman and Superman have fairly consistent love interests in Steve Trevor and Lois Lane, and it's not just tradition why they're a perfect match for their respective heroes. DC's two most powerful heroes need human love interests. Superman and Wonder Woman need that connection to the people they save that a powerless human provides.
More than need though, it's something both characters want. Superman doesn't see himself as an alien and doesn't see himself as above anyone. He loves Lois because she doesn't need powers to do good. Wonder Woman meanwhile did grow up as a princess in a world filled with gods and powerful entities. Diana's character is all about trying to understand the world outside of Paradise Island. Only by falling for someone like Steve can she truly understand the world that normal people live in.
It's telling that most of the alternate universes where Superman and Wonder Woman end up together are bad futures. Though he may have teased a relationship in For The Man Who Has Everything, Alan Moore seemed to understand this, as the unpublished Twilight of the Superheroes depicts a world dominated by Superhero dynasties such as the House of Steel led by Superman and Wonder Woman. Whether consciously or not, DC writers who have been pairing the two have shown exactly why they shouldn't end up together.