The manual for Anarchy Online is the Trope Namer. In Anarchy Online, when you die your consciousness is downloaded into a new body.
In regular Dungeons & Dragons, being brought back from death is a (relatively) rare event that involves a considerable sacrifice of a level and a rare diamond. In Neverwinter Nights, you just wake up in the temple of Tyr when their magic detects that you are about to die.
The Revival spell can do it more easily, but as it has to be cast immediately (like, while the creature that killed you is still right there) and brings them back with 1 hp left, it's not very practical.
In Dungeons & Dragons Online your soul is bound to a dragonshard which can be carried back to a rest point by one of your party. In total party kills the cleric you met in the last tavern you visited calls you back there. Note that in the original soul binding is an extremely evil act and does not allow one to raise the dead without a body.
The Unreal series has an alien technology that raises you from the dead to fight in the Arena some more.
Quake III: Arena does too. It says that the gods wanted more entertainment, so they put you to fight with other opponents, and made you immortal.
This is one of the reasons Team Fortress 2 was designed to be so cartoonish.
The respawn times actually play an important part in balance; on attack/defense maps the attacking team always respawns faster, and on others the timer has to be long enough for death to mean something. An awful lot of servers have instant respawn mods, which plays hell with balance and often makes it less worth killing someone as opposed to hiding from them, distracting them and so on.
In Conkers Bad Fur Day, upon dying for the first time, Conker meets Gregg, the Grim Reaper. Gregg explains that squirrels get "as many lives as they think they can get away with". After stopping Conker when he immediately turns to leave, Gregg then offers to give Conker another chance for each squirrel tail he obtains.
Die in BioShock and you're instantly sent back to the last checkpoint you passed with half health, a little EVE, and all your other stuff.
In the latest version of the game this feature can now be turned off, since it is widely regarded as making the challenge level of the game even at the hardest difficulty a joke (not necessarily a bad thing for players who just want to experience the atmosphere and story, but hardcore gamers get annoyed when the simplest strategy for winning the game is just charging headlong into fights over and over until you whittle down the bad guys through sheer brute persistence).
Note that unlike as usual, in this game the fact that you can use the Vita-Chambers to regenerate and the bad guys can't is major foreshadowing.
BioShock 2 uses the entire concept as a plot point. Delta shoots himself in the head in the opening sequence, but Eleanor used the Little Sisters to take his blood to a Vita-Chamber and resurrect him years later.
BioShock Infinite doesn't have Vita-Chambers. Instead, Booker respawns either by being revived by Elizabeth, or (if Elizabeth isn't with him) reappearing behind his office door and walking back out. Dying, however, costs money, and if you don't have enough money to return from the dead (a big concern when playing 1999 Mode), then it's Game Over.
The pioneering cross-platform Xbox 360/Windows First-Person ShooterShadowrun uses magic to respawn dead combatants. OK, it's magic, but the original Shadowrun tabletop RPG is one of the few magic-heavy settings where resurrection is stated to be flat-out impossible.
You only live as long as someone is keeping you alive, and even then if you die after dying (bleeding out/getting killed after being resurrected or having your body killed) you will vanish into clumps of dirt.
Prince of Persia: The Sands of Time, aside from being able to rewind out of most deaths, invokes this trope when you do die for good as The Prince is literally telling the story. He'll say "That's not how it happened" or some other line and you respawn at the beginning of the room or puzzle.
Before it, Sacrifice used the same point of view. If you fail the mission and restart, the narrator utters a similiar line as above. (Loading the game, incidentally, gets you the sound bite "Now, where was I? Oh, yes...").
In Final Fantasy XI, granting the ability to respawn is implied to be the function of large crystals called Home Points (which are also how you choose where you respawn). The game does not, however, explain why only adventurers can use them...
Parodied in the webcomic Supermegatopia, where it seems to be an established fact in several comics that most heroes and villains don't stay dead.
Also, in the sub-comic Crushed: The Doomed Kitty Adventures, Crushed and other heroes have the Temple of Infinite Lives, which brings slain adventurers with brand new bodies. They are, however, sans the equipment (and clothes) they had at the time of death. This is good, as Crushed tends to live up to her name.
Utilized to a ridiculous extent in Nodwick, where the title character has been killed (mainly by his colleagues) and resurrected over five hundred times. In one particular blatant incident he managed to get decapitated nine times on the same page.
Assassin's Creed I has a very creative system: a frame tale, in which you are Desmond Miles, living several hundred years into the future and being forced to relive Genetic Memories through a machine called the Animus. "Dying" in Assassin's Creed I is basically becoming completely desynchronized with your genetic ancestor, forcing you to restart.
This also gives an excuse for being unable to go into certain areas before you proceed far enough in the game to unlock them. You just don't have those memories yet.
It's possible to die permanently, but most of the time you have to go out of your way to do so (like pissing off an incredibly powerful wizard, or getting petrified.)
The first time you die in Crackdown, you'll get a little spiel about how "Death is not the end." Not only that, but your regenerated body will have exactly the same agility, strength, firearms, driving, and explosives skills will be at exactly the same level they were when you died (minus the token slap on the wrist of emptying each skill bar.)
Possible to be inverted in the shareware space top-down shooter game Escape Velocity. It is possible for the player, at the start of the game, to chose the "Strict" game play mode, which limits the player to only a single death. Unless the player quickly upgrades their starter ship or buys an escape pod, an encounter with a single stray missile means having to start all over again.
Humans are cloned in a chamber that rebuilds their skeletons, overlays the skeleton with organs and muscles, then applies skin and hair.
Apex are cloned in a tube of liquid, then injected with serum that results in them becoming super-intelligent ape men.
Hylotls and Avians have similar ways of respawning: hatching from an egg as a tadpole or chick (respectively) then rapidly aging to maturity.
Florans return as a seed that grows into a plant that produces their new bodies.
Glitches are rebuilt, starting with the torso, then the arms, then the legs, and finally, the head.
When you get caught and put into a death trap by LeChuck in Monkey Island 2: LeChuck's Revenge, you can actually die, if you don't manage to free yourself in time. However, most of the game is actually Guybrush retelling everything that's happened to Elayne, and she will point out that he obviously didn't die, since she's talking to him right now. Guybrush will realize she's right, and explain what really happened, i.e. you get another try.
The Might and Magic series allows you to cast a resurrection spell on fallen party members if you have a cleric or paladin in your team. Barring that, you can always go to a temple and pay to revive them as long as one person in your party is still alive. If every party member dies, from the sixth game onewards you magically "escape death" and wake up with one health and mana in the starting town. Prior to that, if the whole party died, the game was over.
Planetside had spawning tubes in towers and bases that would replicate your body after death, so you could respawn.
In Age of Conan, the player characters' ability to return from the dead is explained as a side-effect of the evil magic that's left mysterious magic glyphs branded on their chests.
In The Sims 3, death has become less of an issue as unlucky and loser sims can't die by accidents and in case you die, there are many ways to return to the mortal coil. And it is a prequel in the sims timeline.
In Grand Theft Auto: San Andreas, your character never actually dies - no matter how much punishment he takes. Being caught in the explosion of a damaged car, falling hundreds of feet onto solid concrete, or collapsing in a pool of blood after being shot or stabbed multiple times never costs him anything more than a trip to the hospital. He simply respawns in front of the hospital several hours later, good as new, though unfortunately stripped of all his weapons (unless he is currently dating the nurse).
Inverted with You Only Live Once, a rare case where death is permanent in a video game. Once the hero dies, you can never play the game again, unless you delete a certain hidden file.
In World of Warcraft you simply have to walk back to your corpse. This is lampshaded by an NPC who sells an (actually useless) item that has flavor text stating it grants this ability. Some fans also jokingly theorize this is why some NPCs are able to be killed dozens of times.
In eRepublik death may not be permanent but being banned for operating multiple user accounts, very much is.
Parodied in Chip's Challenge, where the manual talks about how "Chip is a fragile fellow and dies easily, but persistent, and he'll just pick himself back up and try again" and that Melinda will cut him a break if he dies too many times.
EVE Online explains resurrection as your memories being copied at the moment of death and being placed into a new clone.
Star Wars: Galaxies explains it in much the same way as EVE Online. The majority of NPC and player cities have clone centers, and your clone data is stored whenever you land in a new town or city. When you die, your datapad sends a signal to the clone center to create a new clone of you, complete with all your gear and abilities! Of course, this doesn't explain there are cloning centers everywhere even though the Empire outlawed cloning after the Clone Wars.
A rare aversion in the mediocre rpg Aidyn Chronicles for the N64. You could potentially have a large amount of people to choose from, but if a character died, they died for good, with no way to resurrect them. If the main character died, it was an automatic game over, making combat incredibly frustrating.
The Fire Emblem series has averting this trope as one of its major selling points. Although there are still characters who don't die permanently (in some games, plot-important non-Lord characters will simply suffer career-ending injuries and will be unable to take to the field for the rest of the game.)
City of Heroes explains the player characters' continued survival by the "mediporters" - a teleport and healing system that kicks in when the character's vitals signs go critical. One plot in the tie-in comic involved the villains jamming these so the heroes could be Killed Off for Real.
MabinogiHand Waves this saying that Milletians (player characters) do not die. you are just knocked unconscious, despite the fact that most of the time you get smashed by a giant stone arm, crushed with a giant hammer, or hit with a giant fireball. You may choose how your body gets revitalized, making resurrection a conscious choice.
The fact that you can sometimes take over a dozen times your maximum hit points in damage and stay standing validates this - you can lose consciousness but literally can not receive fatal or irreparable injuries. Milletians can temporarily not be alive (not just unconscious) in-universe, it's just that this can't involve dying as a transitional state. There are a very few things which could cause death (involving some form of infinity), but which player characters are guaranteed to be saved from. And some residents are aware that while Milletians are in no way subject to the local life-death-rebirth cycle, they're not immortal in their true form at home.
In Aliens: Infestation, each Marine has access to whatever weapons and keys anyone on their fireteam has picked up. Sometimes Death Is Permanent, but if a Marine is downed by an alien they'll merely be knocked unconcious and dragged into a hive - where they can be rescued by other fireteam members. That said, once they're rescued, they'll complain about feeling nauseous, and the next time they take mortal damage a baby alien will burst out of their chest. It's unsaid what the aftermath of this is if a rescued Marine makes it through the rest of the game.
Borderlands brings us the "New-U-Station". As soon as you have registered yourself there (can't go on without), those stations, scattered about, save your game when you come near and make you a new you (for a small fee) when you die.
Dragon Quest series features a Crystal Dragon Jesus church system that has a power to revive dead characters in exchange of a fee. The series does not provide a gameover in the event of a Total Party Kill. Instead, you'll be dragged back to the last church you visit and be forced to spend half of your money for a revival.
In the first two installments of Quest Of Yipe, the game ends upon you hitting 0 HP. The third game finally makes death non-permanent by sending you to Hell if you hit 0 HP. You then have to pay the Gatekeeper a small fee before the player is healed up and returned to the game… or you can choose to defeat the Gatekeeper so that you never have to pay any more fees upon returning to Hell, but at the cost of no longer being healed when you leave.
In both TaskMaker and The Tomb of the TaskMaker, you are also sent to Hell upon losing all your HP. In the first game, Hell is a randomly-generated maze to which you have to find the exit, with one Devil hiding somewhere. In the second, you have to do one of four deplorable tasks (rewarding devils with gifts, throwing away large amounts of gold, slaughtering innocent bunnies, or flipping a series of switches that change randomly) before leaving. In both cases, HP is fully restored upon entering Hell, but the player's pouch is dropped.
In the Takeshi Kovacs series everyone has a cortical stack implant that records their brainstate and can be extracted at death for resleeving in a new body. The wealthy have external backups in case their stack gets fried.
That said, quite a number of people (probably) permanently die in the books. At one point the main character personally kills and destroys the stacks of over a hundred people.
Immortality is a central theme of Eclipse Phase. It shamelessly steals cortical stacks and backups from Kovacs but most people's life insurance covers backups.
In Paranoia people are cloned in packs of six, when they die they are downloaded into the next clone in the set.
In The Vampire Diaries, as long as you have a magical ring that resurrects you if your death had a supernatural element (e.g., neck snapped by a vampire) and are not supernatural yourself. There are only two in the series, however; Alaric has one, and Jeremy inherited Uncle John's.
Averted a couple of times, but particularly hard twice: Alaric bites the dust when his life is tied to Elena's and she drowns. She gets better. He doesn't. Also, Jeremy's neck is snapped by Silas. Although he still had the ring, he had since became part of a group of vampire hunters called The Five, making him sufficiently supernatural that it no longer worked for him. This leads to a Break the Cutie moment for Elena, who keeps insisting that the ring will kick in eventually even as Jeremy's body begins to decompose.