in tabletop game which aims to emulate a computer game, and still don't get used to death.
Simplest, most obvious way. Usually some kind of stat or counter that goes down each time the PC dies and once it is zero, the PCs is no longer playable (died forever, became hostile NPCs, etc). Raising this stat is either impossible or difficult. Games like "Dark Souls TRPG" simply limit the counter to three – three deaths and game over. AD&D made PCs to lose either level or Con permanently forever. "Fires Far Away" gives more thematically elegant solution of sacrificing either of three given memories and/or name before turning into NPC, with opportunity to sacrifice a rare item instead (see #6 below). Another game have Humanity stat that almost never goes up but rapidly decreases with each death. In one novel there were humans, descendants of immortals, who could die nine times and everybody knew how many times they still have because a strange bracelet-like-birthmark appeared on their arm with each death, up to nine.
Pros: it gives a defined limited pool and somewhat mitigates the permanent end of the PC life due to bad luck. Death can become a part of planned strategy.
Cons: decrease of tension at the beginning of countdown. Predictability (= possible boredom) similar to how dying was handled in DnD 3.5+PF where the priest didn't have to bother running and healing downed comrade because both know exactly how many rounds they have before downed person dies.
Suggested use: in playtested systems. Larger "deathpool" for more lenient stories, smaller for one-shots or for hardmode.
Random chance to fully die at any occurrence of death. Even in Dark Souls with its infinite computer game lives it is very possible at some point to be too stressed or frustrated to quit forever or break the controlling device. In AD&D something like that was represented by System Shock percentage but there it was still predictable as it was tied to Constitution, so I would suggest to make it a coin flip or give something like 65% chance to everybody to die/survive, depending on how difficult you wish it to be. Optionally modify for terrain and monster (i.e. in poisonous swamps which are so generously spread through all three games or with anything connected to Bed of Chaos I really wanted to go and play Stardew Valley rather for a lot and so I did).
Pros: gives some leeway with dying without (much) decreasing the tension, as each death can be the final one. Equally kind/merciless to everybody. Prevents cheapening of death with resurrection spells when PCs are powerful and wealthy enough to have them at mass.
Cons: still out of control of the player. Still not very interesting as a process.
Suggested use: in systems where resurrection spells might become easily available later on.
PC dies. DM plays anthropomorphic death incarnation. PC wants to go back to life and is willing to try to persuade the death to let them do so. Instead of death it can be a mysterious priest, a devil, the devil even.
Could be and maybe should be systemless, at my opinion, as a pure or almost pure roleplay.
Pros: if people are into role-playing such kind of bargain, it can be a lot of fun to play. Additional quests, curses, brands, geas, all kind of stuff can be added as a part of the process as well as Tarot cards or some other sinister props for immersion and effect. Necromancers and various death-connected occultists get a new interesting aspect to their class as mediators for deceased.
Cons: charismatic or clever players can dominate a meeker DM in such bargain, especially if DM already likes their characters and wants to see more of their adventures. The bargain might go for a while in real time, with a spotlight on a single player, so other players might get bored. Can be trivialized, eventually hand-waved or even turned into a joke. Setting requires to have some kind of psychopomp or an anthropomorphic personification of Death for this option to exist.
Suggested use: if you are sure that as Death-DM you won't let PC easily have their way. If your setting allows for other PCs to chime in in the process of the bargain; in TPKs.
In the first game I've ever played each PC (and probably each NPC as well) had two 'afterfirstdeath' forms (one of necrotic creature and a subsequent one of a specter) before they fully die. Considering that in that game 'Raise Death' spell was available about nine times per life of the priest and the spell only moved the PC one stage 'up', there weren't much clerics willing to cast it just for money so the consequences of dying were still quite tangible.
These forms were, basically, built as templates: a bit like druidic wild shape in sense that there were rules how to build it, and each such form had its own unique abilities, strengths and weaknesses.
A similar but more gradual approach is to give some kind of 'death touch' gift (ability + weakness) on each death. It is similar to countdown but probably more interesting than countdown because with each death something unexpected is happening, almost as with random level up. The overall effect of multiple dying is debilitating, of course, with end result the character turning to some kind of NPC undead creature similar in mechanics on how corruption works in AD&D Ravenloft or in mutation tables everywhere.
[As a variation I use in current Godbox Maze, each time the seeker dies, Pain Saint will resurrect them (whatever they want it or not, most probably), but on successful check PC will get a new ability and on failed check a part of them is simply eaten by the Saint in the process of resurrection.]
Pros: if death gift tables are built well to bring small benefits and not only sheer drawbacks it can be a quite interesting process and, while debilitating on a long run, in short-term it can be even beneficial and less frustrating to PCs. Countdown is still here but not as boring or straightforward as a simple countdown. If death has several stages instead of randomized 'death touch gifts' PCs might get very inventive with their new shapes.
Cons: PCs might want to start dying more often to get perks. Spiral of death (when drawbacks start to overweight benefits). Recalculating abilities more often than with usual levelup (= more bookkeeping). Loses meaning if resurrection/cleansing/atonement spells are quite available.
Suggested use: if you have fast clear rules for afterfirstdeath forms so to apply them quickly. If you have or can make good tables for 'death touch gifts' and like rolling for random mutations.
5. Permanent but with glory
Approach I saw in 'Exalted'. There PCs are very powerful comparatively to normal people and fight gods and demons on almost regular basis but the death is permanent for everybody. This way positions that there is simply no ways to raise a character once they are dead, on any level of power. In 'Exalted' dead PC can technically play a ghost of themselves (similar to #4 above, a separate being generated by different rules) but comparatively to the power level of alive characters, it is a much weaker creature.
Pros: death is very very tangible but due to how powerful PCs it is almost always more satisfactory and/or dramatic than being poked to death by first level nameless monsters or be one-hit by a small town guard in bar brawl due to critical and low HPs.
Cons: In 'Exalted' there are custom charms, and powerful PCs might have a lot of resources to try to invent Raise spells, therefore some DM control is required and grumpy players can happen. Cannot be used in grim and low-level settings.
Suggested use: high-level play where there is no 100% chance to win every encounter.
Death is permanent but preventable with certain rituals which 'redirects' it on another living creature or rare object.
If to speak in Pathfinder terms it is almost like Raise Dead on Contingency but I think it might be especially effective if PCs are duped or almost duped to be scapegoats themselves at first, or have people they care about to be used as such before they have access to such method for themselves.
Only one 'scapegoat' can be linked to a character at the same time.The roots of this method in my memory go at least as far as a myth of Alcestis who was willing to die for her husband (and then Heracles got 'bargain' with Thanatos) but there are probably many other myths like this one.
Pros: the rarity of scapegoats (be it special people, items, ritual components) is fully controlled by DM and their existence or accessibility is not guaranteed. Requires preparation. PCs or NPCs can still be killed if they die a second time before preparing another scapegoat and their enemies will know that.
Cons: PC might find a way to 'farm' the required resource – in live game it is going to be more difficult than to farm humanity in Dark Souls but is still possible without DM control.
Suggested use: never ever ever equal the rarity of scapegoats to increased gp value. Probably best suited for 'evil' parties. For moralistic stories, dramatic stories or domain-level plays.
Probably the weirdest and hardest to handle way, is to reset the time to some threshold in the past and assume that this is now a different timeline where events go slightly differently than before to save yourself a headache to reintroduce everything in exactly the same way as it was before. PCs will lose some progress.
Pros: it gives PC(s) some foreknowledge (which might be not 100% precise) to influence future events and people tend to get inventive with such things. Carefully used alternative timelines can instill a good sense of paranoia or create a mystery that by itself may be interesting thing for players to solve.
Cons: it is pain to erase the progress and technically almost no systems are built to "leveldown" easily. Pain to remember which progress to erase. Pain to remember how everything works. Probably requires flowcharts. PCs who didn't die but still have to reset their progress due to time loop won't be very happy.
Suggested use: if setting or story logically allows this kind of stuff. Probably not in fantasy but in modern occult, surrealism or SF. In TPKs. In one-shots, in systems where level up and level down is easily traceable and/or modular.