The important thing as a GM is to keep your story self-consistent. If someone falls into a lake of boiling acid, or gets eaten by kobolds, she's dead. Short of a GM-hand-wave that fixes everything back up again, your story must continue without that PC.

Which sure sucks for that player.

Solution? Bestow upon a brand new character an approximate match to the old character. This is easier to do if the old character was mostly or completely lost—consumed in a fireball, fallen down a bottomless pit, etc.—because that neatly solves the problem of having too much good equipment to go around in the party. You can transfer over to a new character sheet most of the equipment and character attributes wholesale, then tweak as follows:

  1. Replace the powerful/notable items the character had with different but equally powerful or notable items so there's no question of "how'd you get THAT? I thought the only one in existence fell into a lake of boiling acid?"
  2. Dock the character all of the money and good equipment (read: magical items) that were picked up by other party members, or the party as a whole becomes too wealthy. (Gear and cash that were lost do not have to be docked, they can be transferred as-is.) The "impoverished" character might then make agreements with the other party members to be given or loaned her stuff back, in exchange for the new character doing the grunt work (for example). Don't let this go on too liberally, though. The other characters, properly role-played, might be charitable to a poor adventurer whose help they need, but then again they might not.

    An alternative to allowing swaps between the party members right away works well when the party collects loot and distributes it at the end of the adventure: simply suggest to the other players that the dead character's gear is loot, and should be distributed evenly with the rest of the loot, and the natural tendency will be for the replacement character to get a lot of the original gear back if he has contributed significantly to the party's outcome.

  3. Arbitrarily rearrange the stats a bit. Don't completely reroll, because you'll have a hell of a time getting an equivalent character that way. Just alter them by 4-8 points, adding a 1 or 2 to this, taking a 1 or 2 away from that, so that you have a different but still close-enough character.
  4. Let the player in question flesh out a brand new role for that character - keep class, skills, proficiencies. You may be able to pick a new class kit if it doesn't change the whole character too much, but I don't recommend a brand-new class. Changing race is ok as long as it doesn't change the class or level (due to experience limits on some races). Similarly, changing gender is fine and even encouraged, since it is a simple hook to clearly distinguish the new role from the old.
  5. Make up a background story, including a brief account of how the character went from level 1 to his current level. This can and should be as different from the original character as you like. It helps if the background story results in a plausible explanation for the new character ending up in the same place as the original party.
  6. Most, if not all, of the above work can be done by the player on his own time (perhaps even while the rest of the players are continuing the adventure). There's no need to trust the player to be completely honest about the transfer, because you're going to:

  7. Give the whole thing a once-over, comparing old character sheet to new, and look for any area where major changes were made. Doublecheck that the new character hasn't suddenly gained something great without losing something great. And finally, make sure there are no "wow, that's lucky" pieces of equipment in the inventory, i.e. anything that would give the character an unfair advantage in the campaign where the old character died. If your campaign takes place on a tropical archipelago, don't let the new character end up with a folding boat in his inventory.

After the end of the process of creating an equivalent of the original character, you can optionally then dock the character an item or a couple of attribute points to punish him for getting his dumb ass killed. Most players won't even care about the punishment, because they get the fun of trying out a whole new role.

Finally, remember that the new character has no claim whatsoever over the goods, deeds, name, or titles of the old character. If the dragon left behind a Holy Avenger after he picked the last of the paladin out of his teeth, it belongs to whoever picked it up now, not the new character.

Although this works and keeps everyone happy it is a bit time-consuming. The time consumed is, of course, the time of the person who died, since he's the one who wants back in the game. Ultimately, this whole solution is a deus ex machina, but the important thing is it won't feel like one, because the new character is not the old one, if the player is roleplaying her properly.

Notable notes:

  • This system was designed for use in either a PnP RPG or in the rules for a software RPG, but the original idea came as a way to allow software RPG's something to do with all those dead characters. Character death is far more common in computer games than it is in most human DMs' campaigns, for a wide range of reasons, and it makes playability sense to allow the game to bring the player back from the dead—but how do you implement it without disrupting the consistency of the game world or simply declaring by fiat that resurrection is cheap and easy in the game world? This is one possible answer. A properly-designed software RPG system can handle all of the tasks associated with generating a near-miss character, with the single exception of backstory, which can always be filled in later by the player.
  • This method should not be allowed in either kind of RPG if there is a reasonable chance of the original character coming back into the game. If there's still a corpse, then the body can be dragged back into town and brought back to life. Reincarnation is also an option in some fantasy games.