The being's original body is incorporeal and the physical body is just a (possibly replaceable) tool that allows it to interact with the physical world. This version counts as a form of Immortality, especially if the incorporeal body is Nigh Invulnerable to other incorporeal beings.
The being exists simultaneously in this world and beyond; it really is "dipping" into 3-Dimensional space. These tend to look and actverystrange.
Its awareness is mostly in the form it's taking in this universe; the death of this body merely returns it to its origin point like a rubber band being let go. These type tend to be vulnerable to Deader than Dead if killed at said origin point.
The demons in Mahou Sensei Negima! behave much like those from Dungeons & Dragons. Negi has a spell that can kill a demon permanently, but it's implied something very bad would happen if he were to cast it.
Evangeline uses her "Boss"-level powers to freeze and completely shatter the Demon God that was released during the Kyoto Arc, nevertheless Konoka's father and the other priests still had to reseal it; presumably it would regenerate otherwise.
Albireo Imma uses a more or less indestructible magical projection of himself to guarantee himself a spot in the finals of the Tournament Arc. The only ways to defeat it are to dismiss the projection, or attack his physical body (which is several miles away). Nobody except Kaede (a ninja who uses similar body replication techniques) figures out what he's doing, and admits that she can't really do anything about it.
Later in the Magic World arc, Fate's minions use this to taunt Jack Rakan and Konoka after trapping them in their pocket dimension. Unfortunately for them, they were close enough for Chamo to spot them.
The Heroic Spirits in Fate/stay night are permanently etched into a spiritual domain called The Throne Of Heroes; their "deaths" in any one particular Grail War aren't permanent. In fact, one hero actually attempts to commit suicide by Time Paradox just to get away from existing. It's implied that even that wouldn't work.
Not just implied, he was trying to kill his past self on the off chance that if he were the one to kill himself, the paradox MIGHT just be big enough that he'd be erased. But the "himself" he was going to kill wasn't even going to grow up to be him. Confusing.
Speaking of the Nasuverse the backstory describes several entities known as Aristotles/Ultimate Ones/Types who are a limited sort of Type 2. Even if their physical bodies are destroyed, they still, in a way, exist, and possibly can reform their physical bodies.
As shown in the page image, Gecko Moria uses his own shadow to play this trope literally, invoking Type III; the shadow acts as a Body Double, fighting in his place. It really can't be "killed"; Moria can control its shape at will anyway, so breaking it apart doesn't faze it. Moria can even teleport and swap places with the blasted thing!
In the Sailor Moon manga, after Demand destroys Wiseman, it is revealed that he was but an avatar of the Death Phantom, who has pretty much become one with the planet Nemesis.
The D-Reaper from Digimon Tamers was capable of existing in and absorbing both the digital and physical worlds by creating an unlimited number of mega-level "Agents" alongside a red mass called "The Chaos". Destroying dozens of either barely slowed it down.
In Umineko: When They Cry (When The Seagulls Cry), this is the case if Beatrice and Battler die on the chessboard since their souls exist elsewhere.
In the heavily video game-influenced Beet the Vandel Buster, an immensely powerful Vandel (monster) is defeated by the main character, but it turns out that he was only the "shadow" of the real one, who is, incidentally, trying to become the next The Dragon to the incarnation of evil itself.
It should be noted that ANY Vandel can use this trick, and while the shadow may be weaker, the shadow of an extremely powerful Vandel is much more than even an experienced buster can handle.
Type one used straight and played with in Neon Genesis Evangelion: the twelfth Angel, Leliel, appears as a floating, apparently unkillable orb over Tokyo-3, disappearing and reappearing at will. Turns out its "shadow" is the real angel.
In Magical Girl Lyrical Nanoha A's, the Book of Darkness is like this: every time it is physically destroyed, it respawns somewhere else in the multiverse, ready to devour another planet. The Big Bad's "Evil Plan" includes sealing the Book in magical ice for eternity... along with its current Master. Team Nanoha, however, finds a better solution: separate the Defense Program responsible for regeneration from the rest of the book and destroy it. Even so, however, the Defense Program would have regenerated somewhere within days, had Reinforce, the Master Program of the Book, not committed Suicide by Cop. The Battle Of Aces shows a What If? scenario of what would have happened, had the Defense Program been allowed to regenerate.
The Anti-Spiral from Tengen Toppa Gurren Lagann seems to be something like this. Possible an collective conscience in a shadowy form.
In A Certain Magical Index, Teitoku Kakine becomes like this when his consciousness becomes one with the Dark Matter he creates.
Free from Soul Eater manages to do this by projecting a hologram of himself to stall Death the Kid and Black☆Star, firing a real Magic Eye Cannon at them before they can see him and exploiting his Complete Immortality and ability to No Sell most attacks to sell the illusion. When Death the Kid realizes that he's just tanking ranged attacks but avoiding melee ones (to avoid giving himself away,) he quickly figures out what's going on.
In Dragon Ball GT, General Rildo's consciousness inhabits all metal on his planet. If he is destroyed, a new body is formed from the surrounding metal.
In Chaotic, Aa'une, leader of the M'arrillian tribe, can exist as a weak projection than can still fight but once the player has fulfilled the necessary requirements he or she can flip over the card and Aa'une will become a Game Breaker. Hence this card is an extremely powerful yet fragile Glass Cannon.
Rockslide from X-Men may be the poor man's version of this. His consciousness is some kind of disembodied psychic spirit that controls the mineral pieces of his body (which can explode and reform from nearby earth material at will).
In Watchmen Doctor Manhattan is treated as a Physical God, but towards the end of the story he's revealed outright to be one of these when Ozymandias disintegrates him; he simply comes back moments later (the first thing he learned to do with his new form, as he points out) with a new body and very, very angry. "The world's smartest man means no more to me than the world's smartest termite" indeed.
This happened to Atomic Robo in the Shadow from Beyond Time, where the titular creature kept coming back. Eventually, Robo meets with his fellow time displaced selves inside of the shadow and they detonate a quantum bomb that destroys the creature at all points in time simultaneously.
Final Crisis reveals that Darkseid has been doing this for years, in order to Retcon decades of Villain Decay and justify his many, many defeats at the hands of lesser foes. The real Darkseid is far more powerful and dangerous.
Actually, it has been stated several times over the decades that this is what he's got going, not just in Final Crisis. Grant Morrison is just the guy who remembered he could do this, while many other writers seem to have forgotten. As an aside, the avatars of Darkseid in previous stories seem to be more like clones than this trope, since they specifically say they are not Darkseid and often talk about him in the third person (and not the way Darkseid usually does), to the point where they say they are not as great as him. Though in all other senses they are Darkseid and naturally still consider themselves superior to everyone else, and still think and act and behave like he does. The real Darkseid, for the record, was stuck on the Source Wall for millenia, and had never shown up before Final Crisis except in flashbacks to his younger, usually less powerful self.
Similarly, the Dark Judges of Judge Dredd can take any dead body as their vessel.
In the Darker and EdgierSpace Ghost comics, Zorak has this ability. His species is a Hive Mind with him as the leader, so if Zorak is killed, his essence will take over one of his brethren, which will then physically turn into Zorak.
Batman came up with a way to beat Wonder Woman using a remotely directed chip to get her to fight simulated battles against an equal opponent who never tired. He figured her body would quit before she did.
In Mighty Avengers, a fragment of Shuma-Gorath was summoned and tried to establish a beach-head to bring in the rest of it. The Mighty Avengers still needed to empower and summon a god of their own to defeat it.
In Waking Nightmares, an attempt by the RED mercenaries to find out what happened to the BLU team draws the attention of their world's counterpart to the Big Bad - The Slenderman - who proceeds to slaughter them despite their efforts, even one-shotting the ubercharged (and thus invincible) Demoman and Medic. It's not until Medic accidentally empowers Heavy's weapon with Harmony that they defeat him... and are told that no, that was just a very minor aspect of his true self.
In In The Name Of The King: A Dungeon Siege Tale, the evil wizard Gallian puts his consciousness inside an armored warrior. Every time his avatar is slain, he just laughs and uses a new body to fight.
In The Matrix, the Agents are computer programs working for those running the Matrix, so there's no reason they should stay dead. If you actually manage to kill one by the rules of the simulation, the "body" reverts back to the human it was originally and the Agent program claims a new host (out of anyone still plugged into the Matrix). Double Subversion when Neo destroys Smith at the end of the first movie, seemingly for good by destroying his code itself but ultimately only causes him to become more powerful in the next movie (instead of taking over a host when he's "killed", he can turn anyone and everyone he touches inside the program into another copy of himself, even if they are another program or not hardwired into the Matrix). It's unclear whether his ability to defy true deletion is a general rule (any agent so inclined could come back the way he did) or a property specific to Smith because of how he "died" or who killed him (just like Neo, he defies the laws of the Matrix to return to life when he should have died).
The Lone Power of the Young Wizards series exists mainly outside of time, so the protagonists usually have to be satisfied with only ever defeating the fragments of It which are inside of the timestream. Sometimes, however, the defeat has a metaphysical component which has a permanent effect on the Big Bad.
Sauron in Tolkien's The Lord of the Rings universe. It may take 2-3 millennia for him to come back, but only destroying the One Ring will permanently kill him (and even then he'll persist as a powerless spirit).
All the Ainur (the Fantasy Pantheon of Middle Earth) are like this, with a few exceptions. Morgoth became so obsessed with ruling and then destroying the physical world that he became bound to a single physical body, though even that was still Nigh Invulnerable (rather than risk him coming back, the other Valar cut off his hands and feet and threw him into the void); the Wizards were deliberately bound into mortal bodies to limit their powers so they wouldn't be tempted to fight Sauron directly and risk The End of the World as We Know It (Gandalf was only able to come back with help, either from the Valar or Eru).
Crowley is annoyed at getting shot in Good Omens, as "getting a new body was like getting a pen from a particularly bloody-minded stationary department". Fortunately it was with paint-balls.
Percy Jackson and the Olympians: the monsters and gods are almost impossible to truly kill. Monsters dissolve into sand and pop back up after awhile. The time depends on the monster ex. Mrs. Dodds came back after a few days but some take lifetimes. This is played with with gods in the sense that a god's essence is rarely all in one place. When it IS, they take on their true immortal form, killing any mortal looking at them, but if the greater part of their essence is trapped, they are powerless.
In the Cthulhu Mythos, all of Nyarlathotep's physical forms are merely avatars (or "masks" as they are sometimes called). He is the personification of the soul of the Outer Gods, so whether he actually has a real body at all is never quite clear. Yog-Sothoth (who is one of the aforementioned Outer Gods) is also an example of Type 1 of this trope, as the form in which he manifests is merely the portion of him that intersects that particular point of space and time (Yog-Sothoth exists simultaneously in all points of space and time, or rather, everything exists simultaneously WITHIN HIM. Yog-Sothoth is the PERSONIFICATION of this Trope.)
In Magnus, the title character ends up battling one of these.
Driving the HP to 0 of the Demonlord Tagazin, in the 10th Book of the Lone Wolf series "The Dungeons of Torgar" does not kill him; it just sends him home. In fact, the Remake of the series feels obliged to point out that even if you roll a One-Hit Kill with the Infinity+1 Sword; no, he's not dead. You later fight him on his home turf in a later book; where he can be destroyed permanently.
Many supernatural beings (such as demons) are like this in The Dresden Files; ordinarily when summoned, their spirit arrives in the mortal world and creates a construct body, and if that body is killed, the spirit is simply sent back to the Nevernever (essentially, the supernatural dimension that exists alongside the mortal world). They can be killed permanently in the Nevernever itself, if they enter directly into the mortal world in their true form (as opposed to a construct body), or with certain powerful spells and weapons.
Notably the thirty Fallen Angels are bound to thirty silver Roman coins, yes these ones, who put part of their mind into the first person who takes up a coin and tempts them with power, forcing to use their malevolent powers. Generally people succumb to the shadows of the Angels in their minds and lose their humanity. When Harry becomes the bearer of Lascielnote to save an infant child from grabbing the evil coin tossed at them, what's called her shadow lives in Harry's mind and he battles her temptations and sometimes illusions. He eventually wins by lasting so long, the shadow is no longer just an extension of Lasciel but her own entity and own name, Lash.
In James Swallow's Blood Angels novel Black Tide, Rafen goes up against Fabius Bile — or rather, several version of him. In the epilogue, we learn that the genuine Bile survived elsewhere and Rafen's acts have only hindered him, some.
Some of Stephen King's later works imply that IT is Not Quite Dead after all. IT can never truly be destroyed because IT is an extradimensional entity like the Turtle. All they did was kill its physical form. Logic suggests that, having experienced death, It grew fearful (or at least cautious) of the Losers and only projected Itself into their world again once they were gone, their bond finally used up and forgotten forever. Even if It IS somehow truly gone, there's the implication that some of the eggs It laid were left intact, so glimpses in later works may be It's children...Really, it's only a sweet ending for the Losers' Club. Sure, It won't go after THEM anymore but it's far from dead and gone.
Mythology and Religion
Jesus from Christianity and the Avatars of Vishnu from Hinduism both are said to have been the divine taken physical form. The deaths of their physical bodies did not kill their divine selves. Indeed, Vishnu had ten Avatars, reincarnating every time Evil rose in the world and then accepting death each time once his purpose was fulfilled. Simply trying to define the Jesus/God connection is bound to result in argument, though.
The concept of an immortal soul, either via reincarnation or a true afterlife, implies that this is the case for humans or indeed, all mortal beings, plant or animal.
There is an entire template for avatars to the gods in Dungeons & Dragons. The more powerful deities manifest more than one avatar at the same time; and killing one may only hinder the god itself for a time.
In Temple Of Elemental Evil, killing the Avatar of Demigod Iuz gives you a special addition to the ending where it's mentioned he did return; but the time away meant his plane is in tatters and he's afraid of your party. Also, whether one either drives the Demon Princess Zuggtmoy back to the Abyss for 66 years upon 0 Hit Points or permanently destroys her depends on what actions you take.
Demons in Dungeons & Dragons, if killed in the physical plane, are often merely said to be sent back to their home dimension. In some cases, it takes a hundred years or some MacGuffin to return, but it's not permanent.
3rd Edition introduced the concept of "aspects", which are really just weaker versions of avatars.
Immortals in Classic D&D also use this strategy when entering a world. Immortals are portrayed in Classic D&D as being beyond any kind of mortal power to take on (they are completely immune to all mortal magic and cannot be harmed by any but the most powerful mortal weapons, which do only minimal damage to them) and if by some miracle you manage to take one out on the mortal plane, all you've managed to do is send him back to his home plane. And no one, not even another Immortal, can enter an Immortal's home plane without his express permission.
Mortals can get in on the action, too. "Simulacrum" is a spell that lets you copy a character, although this copy will be significantly (specifically, half the hit dice) weaker than the original. A magic-user can easily copy himself to create a watered-down version of a personal avatar that will obey his every command.
Somewhat like the example with Outsiders, the Astral Projection spell sends the targets' souls into the Astral Plane. If they travel to another plane, they form physical bodies when they arrive, but killing that body simply drives the soul back into the original body waiting in suspended animation where the spell was originally cast. To actually kill the characters, either their original bodies must be destroyed, or the nearly unbreakable silver cord connecting the body to the soul must be severed.
The classic, debuted-in-the-Fiend-Folio creature known as the Berbalang has this as its entire gimmick, with its ability to astrally project duplicates of itself. In 4e it can make these duplicates explode
The White Wolf game line Scion makes use of the Titans as enemies; here portrayed as various primordial or elemental concepts (like darkness, or fire, or fertility) existing as semi-conscious entities the size of entire dimensions. The Titans, being so alien as to not be able to interact directly with the world in any meaningful way, create various Avatars to deal with problems. This is how the plot explains the existence of multiple primordial titan stories from different pantheons (Surtr, the Norse fire giant king, and Prometheus being two titans associated with fire are actually two Avatars of the Greater Titan of Fire, Muspellheim). Suffice to say, the literal avatars of fire or light or water are extremely powerful. Also, if one successfully KILLS one (actual death, not just reforming-later-death) it irrevocably alters the nature of the concept represented by the Avatar. Killing the Frost Giant Ymir wasn't a great idea as it caused the Ice Age to instantly end and flooded most of the world.
In another White Wolf game, Exalted, you have the Primordials, titanic beings that created the setting. Each one doesn't truly exist as a whole, but they have Jouten, which range from Worldbody Jouten, such as the Demon City which is exactly what it sounds like, to Humaniform Jouten, also exactly what it looks like, each of which is an incarnation of their self-hood. Further down, you have their whole hierarchy of souls, a Fetich Soul and its peers the other Third Circle Souls, which are themselves made of souls, Second Circle, and those have minions - which aren't souls - First Circles. Kill a First Circle, there is more where that came from. Kill a Second Circle, that will make the Primordial hurt. Kill a Third Circle, you change the nature of the Primordial. Kill the Fetich Soul and you totally destroy the Primordial. However, it will then reform into something else, which can be very bad, such as was the case with the Lidless Eye That Sees when its Fetich was killed, becoming the Abhorent Prophet Unimagined, who fell into a deep slumber and cannot be reawakened or he will permanently bind everything to the future he sees.
Daemons in Warhammer and Warhammer 40,000 behave like the D&D ones, as their physical forms are merely manifestations of their warp-based nature. Destruction of their physical form merely send them back to the warp.
If you go to its roots, every daemon is effectively an avatar of its respective god, with some of their personality depending on how strong it is (the Greater Daemons are effectively embodiments of the gods' overall personalities, but with their own sentience, while the Daemonic Beasts are effectively mindless), and can be absorbed back into the gestalt whole at a whim. So you aren't so much fighting the shadow of the daemon as the shadow of the god in millions of different avatars (which shows just how powerful the Dark Gods are, considering the strength of your average daemon). On the other hand, the Daemon Princes, who were once mortal, can considered to be this trope played straight - their bodies are comprised of warp energy and, if defeated, they are forced to return to the Warp for a few millenia while they pull themselves together enough to reconstruct their bodies.
The C'tan Stargods can be considered a variant of this. They are immense Energy Beings that normally absorb radiation from stars and are unable to interact with physical objects. The Necrontyr gave them bodies of living metal in which they could manifest and interract with mortals. Destruction of the body does no harm for the C'tan but prevents them from doing much until they get built a new one.
The Eldar Avatar of Khaine, despite its name, isn't quite an example of this. It's an animated construct that houses a fragment of the Eldar war god's essence.
Demons in Feng Shui are the same way. Killing one only sends him back to the Underworld, though if one kills a demon in the Underworld, then the death is permanent.
In GURPS: Fantasy the god Tiamut exists like this. The avatar of hers presented in the book has Unkillable 3 so that if it dies the body vanishes until it returns unharmed with the next spring rain. Meanwhile her real body is half the matter in the universe.
Changeling: The Lost has the True Fae work like this; it's revealed in a book late in the line that the forms the Gentry take on Earth are known as "Titles," and most Gentry have more than one. They're most commonly seen on this side of Arcadia as Actors, but they can be Realms (little pocket dimensions), Props (items of great power) or Wisps (armies of hobgoblins). The Gentry constantly battle against one another for more Titles, and the only way to truly kill one of them is to make your way back to Arcadia and smash the crap out of every one of those titles.
However, if they're truly capable of such an emotion, the True Fae hate losing one of their Titles, and if one of their Titles - particularly an Actor - is in danger of being destroyed, they will often offer extremely powerful oaths to avoid this fate.
Likewise, the Exarchs (essentially, omnipotent god-beings) of Mage: The Awakening are capable of projecting aspects of themselves across the Abyss into the Fallen World, where they take more-or-less physical form. These soul sheaths, or "Ochemata", are still absurdly powerful and are quite capable of doing things like wiping out entire cities.
The above-mentioned Nyarlathotep. The Crawling Chaos is simultaneously a possible Ancient One, a possible Herald, and five to ten separate monsters (depending on expansions.)
Yog-Sothoth is time and space itself, you fight it in game as an Ancient One, a Herald (the Lurker at the Threshold), and every gate in the game.
KULT subverts this: Archons and other superbeings can have multiple incarnate avatars and it take less than one day to create a replacement when one is destroyed. However, getting killed hurts and if several incarnates are killed in short period, the pain can actually kill the being.
Dota 2 has the Fundamentals, beings from "a far upstream plane, where the fundamental laws of the universe have found sentient expression." They can't be killed, as the form slain is only a part that is inhabiting this plane, as stated in Wisp's lore. The two eponymous Ancients, the Dire and Radiant, were feuding Fundamentals that were banished through the stars and eventually caught by a planet's gravity well, eventually shattering their moon prison and raining down upon the earth. They can't be destroyed forever, only weakened, allowing their rival to regain power for a while until the fallen is strong enough to rival it and spark another war. Heroes that are explicitly stated to be Fundamentals are Chaos Knight, Keeper of the Light and Enigma, heroes that are implied to be Fundamentals are Wisp and Ancient Apparition.
The Ancients also have the ability to bring any hero that has fallen for them back from the dead, meaning that, in a way, every hero is this trope.
In The Elder Scrolls, Daedric Lords cannot be killed. All you can do, even if you are the Crystal Dragon Jesus, is send them back to "the voids of Oblivion", from where they will eventually return.
Ditto their associated artifacts: you can unmake one (you get a chance in Oblivion) but it will always spawn back somewhere in Tamriel within a few years.
This is the case with the antagonist Sin from Final Fantasy X, who always comes back after a period of tranquility that has come to be known as "The Calm". In this case, it's a scam to make people think Sin is immortal, it's because the very method being used to "defeat" Sin actually fuels its reincarnation and return. What infected it then infects the Final Aeon that "killed" it.
Your first fight against Omega Weapon turns out to be just a shadow of the real thing, which is further into the cave.
Ganondorf from The Legend of Zelda series fits this trope to a T. Ganondorf appears to be the "physical body", while Ganon is the inner demon essence and a physical manifestation of Ganondorf's true power and rage.
The Reapers from Mass Effect seem to use this trope combined with People Puppets to fight targets planetside. This trope is played straight only really in the second game, however, as killing the supercharged Collector drones doesn't damage Harbinger at all. With the Saren Husk, however...
Harbinger: You only damage the vessel; you cannot hurt me.
That's because Harbinger is using a proxy - the Collector General - ostensibly to avoid what happened to Sovereign.
The Orz in Star Control are heavily implied to be like this. If you can figure out their dialogue. Fortunately, you can destroy their ships just fine if you have to.
If you kill the god Pluto in Phantasie II, he comments on how that didn't accomplish much and he just has to get a new body. You do have his attention now, though. The same goes for killing other Gods like Zeus which oddly enough doesn't permanently annoy them outside of the initial battle.
An interesting variation occurs in Chrono Cross where the Dragon God is just the part of a bigger entity that exists outside time. When you kill the physical manifestation, it gloats that all it has to do is reform with its main self; however it's then revealed that its main self was killed by the Time Devourer long ago.
This is also the reason you can't just destroy the Time Devourer. It will simply switch to/from a different timeline/dimension where you didn't kill it and try again.
Now you know how frustrated the computer feels when you're Save Scumming.
There is also the battle in Vipor Manor, where you seem to fight Lynx and are mocked by the original right after.
As part of a particularly long quest chain in World of Warcraft, you summon the Avatar of Hakkar in the Sunken Temple and trap his essence into some egg thingy as requested by some troll. You can do this as much as you like as he gives you a scroll to keep summoning Hakkar, saying it weakens his true form. A nearby dwarf continues the chain and you learn that actually, you've been making Hakkar stronger by summoning his avatar repeatedly.Woops! Eventually, you do kill the true form of Hakkar, but that happened later than this quest line was introduced. And it's really not settled yet if he's actually dead or was basically just banished again.
According to some quests, demons in the Warcraft universe work like this too. If this is true, presumably the reason Archimonde and pals haven't come back is because it takes quite a while for a powerful demon to regenerate.
This is somewhat backed up by the demon "pets" that players of the warlock class can summon. Whenever they "die" (usually by being defeated in battle against either an AI enemy or a player from the opposing faction in PvP), they are apparently simply banished back to whatever demonic dimension they originate from the same way they are when the warlock actively dismisses them. The warlock brings them back by just casting the summoning spell again without needing to use any kind of resurrection technique like a hunter does for their animal pets.
According to The War of the Ancients book trilogy, Sargeras was already disembodied at the end of the War of the Ancients, when the portal he was using to enter Azeroth imploded while we was inside (as opposed to him getting disembodies only after he possessed Mediev, the last Guardian, and got killed before he could transfer his spirit back to his body). In that case him appearing on Azeroth as an avatar would fit this trope.
In the Cataclysm expansion, Ragnaros, who was killed by players as the first end boss of WoW 1.0 will make a reappearance, his original death being ambiguously a "banishment".
Elementals, same as demons, are considered "Outsiders", and return to their home plane upon "death". Hence the second appearance of Ragnaros in Firelands.
All the above said, Eternals can be killed if they're destroyed on their home world or plane, As Ragnaros learned the hard way at the end of the firelands, when he's been confirmed by Word of God to be permanently dead.
The Shadowlords in Ultima V. Each attack a different town each day; corrupting the minds of those who live there and killing the plant life. Even if one manages to "kill" one in normal battle (which in itself is very, very hard) they reform immediately; as they're really aspects of the Shards of Hatred, Cowardice, and Falsehood. Only a specialized ritual involving their True Name; the Shard they correspond to, and the Flame of the Opposite alignment can destroy them permanently.
In Persona 2: Innocent Sin, the last battle is against an avatar of Nyarlatothep, the Crawling Chaos, who laughs at your efforts and kills a beloved character to prove a point. The semi-sequel, Eternal Punishment, makes things a little more permanent.
In Persona 4Ameno-sagiri is something like this for Izanami.
Explicitly stated what The Stay-Puft Marshmallow Man is to Gozer in Ghostbusters, hence it being banished in the first movie, "killed" in the game, then implied to be killed again by Ivo at the end.
Wraith, the repeating Mid Boss of Phantom Brave is merely a shadow of the true evil, Sulphur. His class is specifically "Dark Avatar."
Killing Sulphur merely sends him back to the "X-Dimension." The Magenta Core can summon him no matter how many times he gets sent back.
The first fight against Ghaleon in Lunar: Silver Star Story is one of these, and his attacks are even suspiciously repetitive. When the reveal is made, cue a domino cascade of going From Bad to Worse when the real one turns up...
Often, killing a summoned creature just sends them back where they came from, and, depending on the game mechanics, may give you a new summon spell.
In one mission in Final Fantasy XI, you get to fight with Professor Shantotto. Win, and "Shantotto" will turn into a doll, only for the real Shantotto to reveal that you'd been fighting with a doll she magic'd into life. She pulls the same trick in Dissidia; when she loses, she turns into a doll, rather than just collapsing like the other characters. Her death quotes range from giving the opponent a B-, to the doll talking in a Creepy Monotone before turning back.
And don't forget Pandemonium Warden, one of the game's two (previously) unbeatable superbosses. When engaging him, he will disappear, then manifest himself as a randomly-selected boss from the Treasures of Aht Urghan expansion. Kill him, he will disappear, then reappear as another boss, and he will do that nine times, gradually moving up the scale from salvage bosses, to beastman kings to high notorious monsters. Only when all those manifestations have been defeated will he appear in his "true form" to face the players fighting him. And even if a group manages to "kill" him, his parting monologue strongly implies he does not truly die.
Final Fantasy Tactics A2 has a few creatures you don't actually defeat, but just prevent from entering Ivalice. One boss battle was against merely the hand of a demon that was sticking into the space between worlds, and it was still several times bigger than your characters. "Killing" it just closed the gap it was using to enter your world.
Julius in Sword of Mana has a literal shadow of himself that often does dirty work that he's not available to perform in person. However, it's apparently not remote controlled, given that it actually asks Julius a favor shortly before the final battle. The heroes still act like they're talking to Julius, though, which is somewhat confusing.
Kefka was a fan of this technique, using it to taunt and ultimately defeat General Leo
Sigma becomes this, after he becomes The Virus; eradicating his current body, his viral self is still intact. Erase it, and a backup copy will pop up later in a new body. It takes killing him on the moon to finally destroy him, supposedly because his viral form will just fade away to nothing with no other robots to infect there. Unfortunately, by that time, an entire army of New Age Reploids were made, all supposedly programmed with a chip containing the DNA of every Old Age Reploid, including Sigma...
In Final Fantasy VII, Sephiroth manages to do this in a number of ways, though he doesn't have any inherent quality of always surviving death. The first times you see him in the game (when you can't fight him, and the characters wouldn't be up to it anyway), it's actually his real body but Jenova's stuff, so killing it almost certainly would not kill him. When you finally get to him for the Final Boss fights, you have to kill two physical One-Winged Angel forms in a row. After that, he was still hanging out in The Lifestream or something and pulled Cloud in to a mental battle. Even after being defeated, he still refuses to be dispersed in the Lifestream like a normal dead person, but instead eventually (in Advent Children) sends out three avatars (who are separate persons from him) to look for what's left of Jenova. When they find it, one of them uses it to transform into Sephiroth, whom Cloud kills again. After that, he's presumably gone for good.
The Sephiroth in Kingdom Hearts is apparently a more straightforward example, an embodiment of Cloud's inner darkness who will always return after being defeated by him. Cloud's fighting his own shadow, in a way. Okay, maybe it's not that straightforward.
In the Legacy of Kain series, you get to be this guy when you play as Raziel. Raziel is a creature of the Spectral Realm, so when he appears in the Material Realm (where most of the story and gameplay takes place), that is just a new body he creates every time he reaches full power. Every time you die in the Material Realm you simply show up in that same spot in the Spectral Realm, and either suck souls to regenerate your health or simply wait for it to happen on its own; once you reach full health you just need to find a portal and you can return to the physical world (and since time in the spectral realm effectively stands still, whatever killed you may as well have thought you just teleported). Die in the Spectral Realm and you will return to the Abyss, and can continue on from there.
In Starcraft II, the hybrid, when killed, will regenerate by siphoning power from trapped protoss.
Midway through Shin Megami Tensei II, you fight against YHVH, aka God. Except it's not the real one, it's just a false image unconsciously created and empowered by the archangels. In the end, if you're not choosing the Lawful path, you fight the REAL one. And even if you win, He says He will not truly be defeated - as long as there are people praying to him, he will return.
The same holds true to any demon or god in the series. Killing them doesn't stop them from showing up in any of the other games, or even later in the same game. (Often it gives you the right to summon them as Mons.
SNK's Fuun Series games (Savage Reign and Kizuna Encounter) feature King Lion as a playable character. Of course, he's actually just a shadow of the real boss character King Leo. Indeed when you beat King Lion in SR, Leo mocks you before challenging you himself.
King Leo: Hahahaha! Did you really see all of the King?! He's just a shadow! Now you will know who's the strongest!
Hydreigon in Pokémon Mystery Dungeon: Gates to Infinity is actually a Nature Spirit known as the Voice of Life, who's taken a temporary physical form as a Pokemon for the sake of protecting the world. His body ends up getting totally annihilated by Kyurem, but this only serves to keep him aiding the heroes in the final battle, as he returns good as new in the ending and laughs off what happened.
In the early webcomic Argon Zark, when Zeta deletes the monster Badnasty Jumpjump, the robot Cybert comments "alias deleted". The real Badnasty is still present.
Parodied by RPG World. The Big Bad knows that the band of heroes is going to storm his fortress, so vacates it and leaves a Shadow of himself behind to fight them. The good guys know that it's just a Shadow, but Hero insists on defeating it anyway.
In Digger, when Shadowchild meets with and eats a shadow of Sweetgrass Voice.
As a Dungeons & Dragons lich, Xykon of The Order of the Stick is like this- if his body is destroyed, his soul will simply retreat to his Soul Jar and create another one, rendering him nearly impossible to kill. Of course, it made things a lot harder for him when his Soul Jar went missing, but then it was found again.
The Bloodgrem from El Goonish Shive. It can't be killed, only "un-summoned", and it can always be summoned again.
Nanase can summon a fairy version of herself which her mind can inhabit. If it is destroyed while she does so, she gets traumatic feedback from it, but her mind is returned to her body, and can then summon another fairy.
Petey did a bit of this with holospheres in Schlock Mercenary, although the third hologram transmitter was also rigged as a bomb, following Petey's "three strikes"note as in baseball policy.
This is explicitly how at least the more worrisome types of demons (like the one Phase fought in 'Ayla and the Grinch') work in the Whateley Universe. It's one thing that distinguishes them from devils, which are more like evil spirits that exist in the here-and-now in this setting.
An interesting variant occurs in Worm with Oni Lee. Whenever Lee teleports, his new body is formed at the target destination and his old body continues on for several seconds before dissolving into carbon ash. But those seconds can be a long time in combat...
There's also The Siberian, who is eventually revealed to be a projection created by William Manton
This is how the Avatar in Avatar: The Last Airbender normally works: the Avatar's existence is mostly in the spiritual world; and reincarnates into one person at a time. This trope is actually inverted when in the Avatar State; by pulling all of itself into the physical world, the current Avatar wields tremendous power, but if he should die while in the Avatar State he'll have no way of reincarnating.
To clarify, if the Avatar dies in the Avatar state the Avatar Cycle will be broken. The World Spirit will not necessarily die, but the Avatar Cycle will have to start over again. Each Avatar draws on the strength, experience and power of their predecessor, especially in the Avatar state, so this would be quite a major handicap, but it would still not mean the end of the Avatar, only his reset.
Also should be noted that individual Avatar's are utterly powerless when they actually go to the Spirit World where the World Spirit (i.e. the Avatar itself) originates. So inverted a bit in that the Avatar actually gets stronger by appearing in human form (sort of, anyway).
Big Bad Van Kleiss of Generator Rex was originally human, but his consciousness now resides in the nanites that infuse both his body and the area around his stronghold- which means that even if he's "killed", the nanites can just generate a new body for him straight from the ground.
Brainiac in Superman: The Animated Series. Even the smallest piece of him contains his complete consciousness- and he always has a back-up copy of himself stored somewhere. As such, he's one of the few opponents Superman will use lethal force on, because the Brainiac you can kill is always just one part of the whole.
This is illustrated very creepily in the Justice League episode "Twilight", where Hawkgirl smashes Brainiac to pieces, apparently killing him- only for the team to be immediately surrounded by dozens of identical Brainiacs, all of which are identical extensions of the central consciousness. Yikes.
However, after that only a small fraction of him survived in nanobot form inside Lex Luthor, and the rest seemed to be his equivalent of spiritual essence. When the former was destroyed a fragment remained, but it was powerless and seemed to be genuinely dead. The latter was fully reformed in the Grand Finale, but only as part of a resurrected Darkseid. His personality is now totally subsumed by the latter, and the latter was destroyed and even if he comes back, currently this Brainiac can be considered Deader than Dead.
And yet, Brainiac 5 must've come from somewhere. Not to mention the episode in Superman The Animated Series where he came from the very far future to destroy Superman before he even learned about his powers.
The death of anyone in Transformers who is considered to be a "multiversal singularity" is considered to be this, so don't count Unicron, The Fallen, or Vector Prime out just yet. Mind you, it is an All There in the Manual thing and within their series, there is nothing to hint their survival - when shown to be completely destroyed. (Blow Unicron up but leave the head? He'll be back.)
To specify, they are both extremely hard to actually kill rather than weaken, and, once you do actually kill them, it doesn't stick. They've long since learned the ins and outs of cross-multiversal existence, and periodically spend time in reverse-time universes, which basically allows them to save their e Spirit game and resume from there when a physical body kicks it, as the consciousness just jumps to the concurrent body in the reverse-time universe, which retroactively becomes their "true form", despite having been a past/future self a few minutes ago. So, essentially, they revive themselves by telling causality to suck it.