We all know Batman practices a No-Kill policy (though he still kills in the movies), so does Superman also have a no killing rule?
After all, Superman is supposedly a sign of hope, so it's just not right for him to kill. I think it's all right if you exclude the DCEU because he killed Zod.
He has been shown to kill as a last resort when he feels there is absolutely no other option.
Superman issue 22 (1988) was the end of a mini-arc where Superman had been brought to an alternate Earth where Zod, Quex-Ul, and Zaora had killed everything on that version of Earth (literally everything: they'd rendered the planet lifeless except for a few holdouts in an isolated fortress). The last few survivors, who included alternate versions of people Clark knew like Hal Jordan, died in a final battle to defeat the three Kryptonians, who Superman ultimately depowered using that dimension's gold kryptonite, leaving them the only four living creatures on the planet. Although defeated, Zod swore they'd get their powers somehow and then they'd find a way to Superman's dimension and do the same to his Earth.
Individually, they were stronger than him[1] and, if they somehow made it to his dimension, they'd be immune to the kryptonite there just as he was to theirs, leaving pretty much nothing to stop them. He decided his only option was to execute them with green kryptonite. Which he did.
This led into a long arc where the deaths caused him such mental trauma that he exiled himself from Earth when he returned home to try and deal with what he had done. This led directly to the introduction of WarWorld and the modern version of Mongul, who he encountered during his self-exile.
In the DC animated universe, in Batman Beyond (1999), episode The Call, at some point, the Justice League suggests killing methods to get rid of "Starro", an alien starfish-like creature that can take control of the people it attaches itself to. During the discussion, Superman said they can't just kill them, to which another member of the League commented that he's back to his old self.
Big Barda: So, where should I boom them to? Some empty galaxy? Or maybe the surface of the sun?
Superman: Barda, these creatures never asked to come here. We have no right to kill them.
Warhawk: Back to his old self again.
But at the same time, earlier in that episode, when Batman was in a dangerous and critical situation (when the starfish creatures were about to escape into the ocean, possibly overtaking the entire Earth), Superman was ready to sacrifice Batman to save the world. Although, in this case, it can be argued that he also had faith in Batman being able to get out of the situation alive.
Big Barda: Kal, what are you doing?
Superman: Aquagirl must have opened the gate. I've gotta block it.
Big Barda: But Batman's down there!
Superman: He knew what he was getting into.
In the same continuity, in the animated series Justice League Unlimited (2004) (which happened before Batman Beyond in the timeline), episode The Doomsday Sanction, the Justice League decided to banish Doomsday into the Phantom Zone in order to prevent him from going on a rampage, whilst also avoiding killing him, to which Doomsday said they're going to wish they killed him instead of merely making him a captive.
Superman: I only use this as a last resort. It's gonna send you to another dimension. You won't be hurt, but you also won't hurt anyone else again anymore.
Doomsday: You'll wish you killed me.
However, in the animated series Justice League (2001) which happened before Justice League Unlimited, in the episode Twilight, Superman was about to finish it once and for all with Darkseid. Although the place where they were located was about to blow, he refused to leave. Not without killing Darkseid.
Darkseid: You really are a glutton for punishment. Time and again I've beaten you, humbled you. What makes you think today will be any different?
Superman: Because this time I won't stop until you're just a greasy smear on my fist. Let's go.
Batman: Superman!
Superman: Go! I'm finishing this.
Batman: Kent, don't be a fool...
Superman (after violently brushing Batman away): Get out of here! NOW!
Although he was mostly pushed by his hatred towards Darkseid (since the latter used him, tainted his reputation, then double-crossed/betrayed him), it is one of those occasions he seemed to be willing to kill. In the end, the explosion ended up killing Darkseid who couldn't escape. But on the instant, Superman didn't want to take the chance that he might survive.
This suggests that he tends to have a no-kill rule of some sort; or at least he avoids it when he can. But he's also fully capable of committing himself to killing if he wanted to.
Superman, like Batman, is a hero who generally doesn't like to kill. He tries to stop bad guys and save innocent people without taking lives.
Some examples:
In the comics Superman: Red Son, Superman uses his heat vision to melt the guns of criminals, instead of killing them, as a way to incapacitate them.
In the episode "Apokolips...Now! Part 2" of the animated series Superman: The Animated Series, Superman uses his freezing breath to freeze Darkseid's troops instead of killing them, as a way to incapacitate them.
In the episode "Escape from Bizarro World" of the animated series Superman: The Animated Series Superman uses his heat vision to melt the chains that held Bizarro Superman captive instead of killing him, as a way to free him.
In the Superman films, Superman's no-kill policy is not as clear-cut as in the comics and animated series, probably because movie audiences expect a different tone, but he still tries to avoid killing whenever possible. Superman's no-kill policy is as absolute as Batman's, and there are times when he has been forced to make difficult decisions, and in some cases, take a life. But it's clear that in most of the cases, Superman tries to avoid killing and finds non-lethal ways to stop his enemies.
Even in the animated series, while he doesn't kill directly, he's sometimes responsible for deaths, for example where he left Darkseid for dead in his exploding HQ.
