Following in Moorcock's example, every single monster in the various Monster Manuals of Dungeons & Dragons, up to and including demons and horrors from the Far Realm, can be defeated by bashing it to zero Hit Points (in every edition).
Not all of them can be attacked with normal, everyday weapons, however. Some can only be defeated by spells and magic weapons.
Both the first edition and third edition of D&D's Deities And Demigods assigned hit points and combat statistics to god-like beings. The d20 Call of Cthulhu, a sister product to D&D, allows players to specifically fight and to kill Elder Gods. Their stats are tough enough that only epic D&D characters — themselves nigh-unto gods — could stand a chance against them, though. (Monk classes fit this trope literally: Being unarmed classes, an epic-level Monk could REALLY punch out Cthulhu.)
Cthulhu himself was statted up in First Edition, and could actually be taken down by "normal" high level characters - powerful, but still thoroughly mortal.
Averted in the 3.5 book Elder Evils with at least some of the evils. They don't have stats and can't be fought directly, you can thwart efforts to rouse them or make them manifest. In some cases, this does involve battling their spawn which are statted but still usually require high level or epic level characters to beat. If one of the actual Elders does arise/manifest/wake up, the world is screwed.
Averted by the Fourth Edition. Evil gods are given full stats, but they ignore attacks by characters who are not themselves also epic level and thus on a path towards immortality themselves. Even with damage from an epic-level threat, they cannot be killed by normal means, as they "discorporate" when they take enough damage to be considered bloodied. Each god's listing comes with a few idea seeds for ways the being might be slain, but that's left to the dungeonmaster's judgment. Lower-level "aspects" of the gods can still be punched out, though.
Note, however, the rules for killing the Tarrasque in Dungeons and Dragons. First you reduce its HP to 0. Then, to make it stay dead, you cast Wish. If, as is sometimes done, the spell is removed as a Game Breaker, the beastie is coming back no matter what.
There is a collection of D&D jokes somewhere on the Internet that invokes this trope. "You know your character is too powerful when...". In particular, there was the series on jokes about the demon lord Orcus, who was in the early Monster Manual stated to be so strong that he'd deal damage with a slap with his open palm. The jokes went something like this: "You know your character is too powerful when... ... You slap Orcus on the back, and Orcus dies. / Orcus slaps you on the back, and Orcus dies. / You think "Maybe I should kill Orcus" and Orcus dies..." And so on.
Handily averted by just about every other Call of Cthulhu RPG. In the original rulebook by Chaosium (and from 2nd Ed. onwards), Cthulhu's stats are so high that he's essentially Nigh Invulnerable (although a big enough attack, say six tanks firing at once, has a reasonable chance of dropping Cthulhu for up to 20 minutes), and he "devours 1D6 characters per round"; in the GURPS version Cthulhupunk (which mixes modern-day Call of Cthulhu, Cyber Punk and High Tech Sci-Fi genre), a note indicates that vaporizing the big guy with an A-bomb would only get rid of him for two days, after which he would return... radioactive.
In the early Call of Cthulhu by Chaosium the Headbutt skill allowed you to stop anyone acting for one turn. A starting character had a 95% chance of pulling this off. Apparently, even Great Old Ones are affected by the Headbutt. (Most versions of the rulebook mention that non-humanoid creatures are completely immune to all knockout attempts.)
In Warhammer 40,000, the C'tan Physical Gods just need new bodies built for them if the shells are destroyed, although it is said that neither of the two active ones are at full power yet.
The C'tan can actually be Cherry Tapped to death with sniper rifles, due to their crappy save and sniper weapons always wounding half the time.
The new Necron book has Retconned this backstory so the C'tan, with the possible exception of the Void Dragon (who is implied to have been punched out by the Emperor), were ripped several dozen new ones by the Necrons, with the star-gods reduced to fragments rather like Khaine. Only worse, since Khaine was destroyed by other divine beings, and the C'tan dismembered by robots. We assume their expressions were rather like that of a chess player being beaten to death by their own pawns.
Eisenhorn managed this one throughout his career, but the most notable is when he destroyed the daemonhostProphaniti so thoroughly that even its warp presence was extinguished. With nothing more than a force staff and his own balls-out badassness.
The Ultramarine Space Marine Chapter Master, Marneus Calgar literally punches out the Avatar of Khaine, the bloody handed war god of the Eldar.
On a similar note, Ragnar Blackmane of the Space Wolves manages to single-handedly stop Magnus the Red, daemon prince of Tzeentch and primarch of the Thousand Sons legion, from entering the material realm by throwing the Spear of Russ right into his eye and thereby closing the portal that was threatening the planet. Oh, and is it worth mentioning that he was still a Blood Claw when it all happened?
Worth mentioning that when their paths crossed again, Magnus remembered that last time. Same Wolf, same weapon and same intent. Our one-eyed Primarch buggered off just as Ragnar was about to throw the Spear, thus saving the system in a general sort of way.
In the Fire Warrior game and the novels based on it, the Tau manage to defeat a Chaos greater daemon. In the book, it's killed by a team of Mini-Mecha, in the game it's killed by Kais himself. Alas, Kais goes a bit off his trolley afterwards, but hey, not many beings in the setting can boast about taking on a greater daemon single-handedly and coming out on top.
In the lore, Skarbrand tried to do this to Khorne after being prodded by Tzeentch into thinking he's more deserving of the title "Blood God". Khorne's reply to this is exactly why Skarbrand is the sole Bloodthirster unable to fly.
In Black Crusade, the roleplaying spin-off for Chaos-worshipping characters, a sample Slaaneshi daemon princess is an Empowered Badass Normal who did just this. Known as the Thrice-Possessed, she summoned three Keepers of Secrets into her own body sequentially, and each time she did so, she reversed the possession, enslaving them and drawing off their power until she completely drained them. For a bit of perspective, a Keeper of Secrets is an Eldritch Abomination that is so mind-rendingly beautiful that most people will, upon seeing one, fall to their knees and beg for rapturous death at their hands, and normal daemonic possession is a Fate Worse Than Death for the person possessed.
In the backstory, the mortally wounded Emperor finally realized that Horus was beyond saving after witnessing Horus casually murdering a man (by psychically flaying him alive) who was absolutely no threat to him. The Emperor then unleashed a psychic bolt at Horus that was so powerful that it sent the four Chaos gods who were possessing Horus fleeing back to the Warp. While the Chaos gods survived, they notably haven't taken as active a role since.
Exalted has a good number of ineffable, horrifying beings out there on the periphery, all designed so that your characters will inevitably beat the snot out of them. A lot of gods in Exalted are weak enough for starting characters to kill them without much trouble (granted, many gods are "Least Gods", whose dominion encompasses things like individual blades of grass). Scion, by the same company, follows the same design philosophy.
The quotes page for Exalted contains this gem, apparently found on rpgnet.
To elaborate: Titans in Scion are less like living beings and more like worlds unto themselves (they do have minds, but like A'tuin the Great, they think thoughts so huge and slow that lesser beings cannot hope to comprehend them), floating in the Overworld, with landscapes, cities and entire races of monsters within them. Each one of them represents (and is naturally ruled) by a certain basic element of reality, and its existence ensures the continued existence of the element. Any attempt to Punch Out a titan would result in breaking the World's arm. Killed the titan of fire? No more fire or heat in the universe. Killed the titan of darkness? Now the entire universe is filled with endless, blinding light for all eternity.
The tabletop roleplaying game Cthulhu Tech, which is a mashup of Neon Genesis Evangelion and Call of Cthulhu, both averts and works this way. The Old Ones themselves pretty much automatically win if they actually bother directly fighting any number of protagonists, and the awakening of Cthulhu would officially screw over not just the human race, but an alien race trying to invade as well. Even the avatar of Hastur, horribly crippled to work within our limited sets of dimensions and weakened by improper summoning, is set as outgunning every other army on the planet combined. Thankfully, he stays at home. On the other hand, you can easily beat up a few Humongous Mecha or even an Engel with luck and some simple soldiers, or survive exposure to the infinite dimensions without being fried instantly. Seeing an Old One directly can't even drive you irreparably and instantly insane on its own, and lucky individuals can stroll up to the body of Cthulhu, take a picture, and leave without taking a single point of insanity.
Munchkin has a Cthulhu version, as well as a variety of others. It has been stated in the Internet-based epic rules that with these rules in play, at high levels, you can have enough personal power to kill a radioactive Cthulhu and his clone. Presumably, by this point you have six hands, and they're all on fire.
Monsterpocalypse features the Lords of Cthul, who have "We were inspired by HP Lovecraft" written on them in the maddening tongue of R'lyeh. Complete with tentacles. In the backstory, they're avatars of cosmic forces and are here simply because they like making people dead. These avatars can be taken out by tank fire, kamikaze cyborg alien birds, and 60-foot-tall Highly-Visible Ninja bodyslamming them.
In Witchcraft, humans can grow powerful enough to eventually take on Gods, Archdevils, Archangels, powerful monsters, and other horrible things from beyond. However, special mention goes to the non-magical dreamer guy that crushed a god. Turns out taking on a lucid dreamer in the dreamscape is a good way to get yourself killed, no matter what you are.
In Magic: The Gathering, this can happen to the players themselves. See, you are a "planeswalker," which is basically a wizard with godlike powers. And a life total. Most creatures with an attack power higher than zero can, if left alone, bring that total down to zero, effectively "killing" you. Now, this is perfectly acceptable when the creatures are angels, demons, dragons, elementals, and so forth, but becomes a little stranger when we start talking about elephants, lions, tigers, and bears (oh my), and becomes outright ridiculous when insects, rats, squirrels, and little girls enter the picture.
With the advent of planeswalker cards (which represent ally planeswalkers assisting the player in battle), Wizards has started printing cards that punch them out for Competitive Balance reasons. Ironically, their most recent effort, Vampire Hexmage, is seeing play in pro-level tournaments mostly due to her ability to summon a near-equivalent of Cthulhu (who can defeat a player character in one attack).
To be fair, most of those "wimpy" creatures will only be able to take out a Planeswalker if he is actively ignoring them in favor of fighting another Planeswalker, or if they are receiving backup from another Planeswalker. The player has hundreds of ways of killing or erasing from reality virtually anything effortlessly if they were willing to devote the resources to it and it hasn't been granted a form of protection, not just creatures but also landmasses. Though that just makes it even funnier that one of the most powerful strategies in the game is to just swarm the opponent with goblins and more goblins until they beg for mercy.
It's worth noting that this wasn't possible for the original Planeswalkers, who were even more powerful than the godlike wizards that exist today — duels were essentially just a game for them, and life points were part of the rules of that game, rather than an actual representation of their health. An in-universe event ended up massively reducing the power of Planeswalkers to the point that they can actually be punched out.