The comic canon character of Superman does his absolute best to avoid killing other sentient life forms. If we were playing the Hero System games, his power limitation would be Code Against Killing, full time, absolute, complete with psychological breakdown if broken. With very few exceptions in his very long history, Superman did not kill his enemies.
Strangely enough it was not always this way. Early 1940 Superman was much less discriminating in his handling of mobsters and other reprobates, threatening them with great physical injury unless they complied.
It was early in the 1950's where he started getting his squeaky clean Boy Scout reputation complete with his Code Against Killing. Now part of this was due to the Comics Code Authority which mandated particular behaviors so most superheroes during this time cleaned up their act.
Superman is a bit less discriminating with robots (which explains why many of his enemies in the Max Fleisher's films were unintelligent robots. Back in the 50's and 60's artificial intelligence was much less well known so Superman treated anything which considered itself living to be so and was reluctant to kill them as well.
Superman's code against killing was nearly absolute during the Silver Age and wasn't effectively challenged until the Post Crisis (Superman #22) where Superman confronts the Phantom Zone villains from a parallel reality.
These Phantom Zoners murdered all six billion humans living on their world and were seeking a path to other realities. Superman confronts them, passes judgement for their crimes and kills them with Kryptonite from their reality (harmless to him).
This is his most famous act of judgement until he battles the monster Doomsday, where he and the creature battle each other to a standstill and kill each other with their last simultaneous blows.
There are alternative universe versions of the character which have killed, the most infamous of these is Superboy-Prime. Superboy-Prime slaughtered his way across the DC Universe until he was imprisoned in the Source Wall.