I feel a description and discussion of Doomsday's history, powers and characteristics are important to include here, as it sheds some light on how he was able to "kill" the Man of Steel. While there is no erroneous information in anm's writeup, I feel his broad strokes miss the crucial details that explain the true threat Doomsday presented and why he was the one who finally bested Superman.
Doomsday is the result of an alien genetics experiment, however noders may find it interesting to note that he was raised on Krypton, Superman's old stomping grounds. He was a project dreamed up by a somewhat mad geneticist named Bertron who travelled to Krypton in search of the perfect environment to engineer the "ultimate being". Bertron began by constructing himself a laboratory complex in the harshest regions available on Krypton, shielded from the extremely high temperatures and ravaging winds by a protective dome. Doomsday began life as an alien infant Bertron discovered with some resistance to the harsh environment. Bertron brought him to his lab and simply kicked him out of the dome to fend for himself as the good doctor observed the results. The infant was almost immediately eviscerated by the ferocious and bloodthirsty ceatures that inhabited the volatile region, but Bertron retrieved what little tissue was left of him and made a clone from the remains. Once the clone had come to term he was back out on his ass outside the dome, where he was again shredded and devoured, only to be cloned again to do the whole thing over. This continued for a very long time, but slowly the creature began to adapt and evolve in response to this torture. After thirty years he was completely at home in the volcanic environment and had evolved enough to provide good sport for his hunters for a few hours before being slaughtered once more.
After a great deal of time had passed, Bertron began to see the results he was looking for. His creation became a force to be reckoned with, and turned the tables on his former persecutors by hunting them into extinction in only a couple of years. Bertron took to referring to his creation as the Ultimate and was most pleased with the results of his tireless decades of cloning. His satisfaction would not last long, however, as the Ultimate's next project became returning the favor Bertron and his team of scientists had been doing for him every day for years on end. This became simultaneously the end of Bertron and the beginning of Doomsday.
After acquiring a supply shuttle that had been lying around the lab, Doomsday took off for parts unknown, mostly just shooting aimlessly around the universe and wreaking havoc on unfortunate planets that got in his way. Although he occasionally met some impressive resistance, no one seemed capable of doing any more than slowing him down for a brief while. At one point the Guardians of the Universe dispatched thousands of Green Lanterns from across the cosmos to stop Doomsday, who was largely unimpressed. He slaughtered Lanterns by the hundreds and grievously injured a healthy majority of the survivors. Finally one of the Guardians managed to cause an explosion big enough to send Doomsday rocketing through space once more.
Eventually Doomsday floats around space long enough to run into Earth, where he catches a whiff of Kryptonian blood from our Big Blue Boy Scout. Doomsday immediately begins a rampaging search for Supes, and as usual destroys everything in his way. He's a destroyer. That's what destroyers do. But so anyway he eventually causes enough of a stir to get Supes' attention (after bitch-slapping the Justice League ), and the epic battle ensues. This is the important part though, because it's where we finally realize the scope of Doomsday's power. When they first meet, Superman doesn't have too much trouble subduing him. Problem solved, on to the next thing. Except that Doomsday comes back, and oddly immune to whatever killed him previously. No biggie, Supes has a couple different tricks up his sleeve. But Doomsday comes back after everything. At some point in the endless decades of being killed, cloned, evolved, killed, cloned, evolved ad nauseam he figured out how to do the comeback part himself. So sure, you can kill him, but he'll be back. And whatever you used to off him last time - be it frosty breath, heat vision, phenomenal strength, a quad laser, whatever - now it tickles. And not that much. Superman had finally met his match. Eventually he ran out of tricks and had to resort to a good ol' fashioned brawl, and after centuries of bouncing from planet to planet like some kind of malevolent pinball, Doomsday was no glassjaw. It took everything Supes had to put him down, and after he pulled it off, he dropped down dead like ol’ John Henry.
So of course here come four new Supermen (the alien, the cyborg, Superboy, and Steel) and one of them (the cyborg) takes it upon himself to strap Doomsday to an asteroid and let him float around space for a while, cuz that always solved things before, right? Of course Doomsday eventually gets free, chaos chaos chaos, destruction destruction destruction, yadda yadda yadda, Superman flies to crazy far corners of the galaxy with some kind of magic box that enables him to fight Doomsday off once again and trap Mr. Meanie in the end of time. Typical super-plausible comic book solution.
But the point here is that while it may have been a little irreverent on DC's part to kill Superman with perhaps the craziest deus ex machina ever conceived, you can't knock them for not taking the death of Superman seriously. They invented what is potentially the most powerful creature in comic book history and gave him what is surely the most convoluted back-story ever just so Supes' death would be plausible. I mean, come on. We all love Lex Luthor , but who really thought an old bald guy was ever going to pull the big one over on Superman? It all boils down to this: say what you want about DC writers, but you have to admit— Doomsday is One Bad Mother.