One mechanic I think could be added back in at least some games is the old Oregon Trail method, just leave a reminder of it. Die somewhere out in the wilderness of Red Dead Redemption, come back later and find a grave in that spot or some old bones. Grand Theft Auto? Chalk outline, police tape. Other games like Dead Space could stack up actual corpses, not the player's but after a few tries you start to notice the stack of dead bodies seems to be growing along a particular hallway you can't get past, just throwing it in your face. Obviously this only works with certain games and within certain limits so you don't have 100 bodies or police crime scenes scattered about town, but I think it'd be a nice little reminder to stick it to the player, especially if it's made where those markers are there even if they reload an old save.
Alternatively I would mark the player themselves. Much like Prince of Persia who started out in his royal regalia but gradually stripped down over the course of the game, but in this case it's from death. Start out in a full suit of knight's armor, glowing wizard robes, high tech combat armor, whatever, and as you die it makes a visual adjustment each time. Doesn't change your stats or game mechanics, just your player and outfit look a little worse for wear each time, racking up scars like Fable, slashes in clothes, dents in armor, bloodstains. It would give people something to work towards to make it all the way though with their gear intact.
You could even apply this to the gameworld at large instead. Take Kirby's Epic Yarn for example. Every time Kirby dies on a level and comes back, have the colors more muted, the fabric looking more tattered, stained, falling apart, enemies looking a bit more menacing without actually changing how they act. Just a visual reminder of 'hey, you screwed up and now the whole world is a bit worse for it.' In something like that you could reset it each level back to the 'default' sunny and cheerful.