I really like persistent elements in roguelikes, because they give a feeling that each game is bigger than just the character and the randomly generated level.
Nethack has "bones files", where if you die on a non-special dungeon level, there is a chance that the level is saved along with your dead body, your stuff, a ghost and a tombstone telling how you died. On an active server like nethack.alt.org, you can expect to find two or three former dead adventurers during a game. Crawl does something similar, spawning badass ghosts of former adventurers as you explore the levels. Especially in Nethack, these "bones" liven up the (admittedly) rather plain dungeon levels.
You Only Live Once has a different take. You start as a small kid who's exploring the woods near his village. He finds a dungeon, goes down it, and has to fight monsters. Then he dies.
And then you get to play as the kid's (adult) neighbour, who's looking for mushrooms for his wife. Next up is the first kid's mother, who finds her kid eventually. And it goes on like that. I suppose you run out of villagers eventually - I only played through once and won as the village elder.
Dwarf Fortress takes that same concept much further. When you start the game, you have to generate a world with a few hundred years of history (or download a pre-gen). Then you generate an adventurer in that world and talk to people who have relatives and history stretching back through time. Some of them will send you on quests to kill beasts who they have legitimate grievances with, because the world generation simulated the beast's pillaging of the local countryside and all the fights it fought. Nuts.
What I'd love to see is something as expansive as Dwarf Fortress with the interaction from Nethack. Not a cooperative MMO like Wurm Online, but the Dwarf Fortress Clone would run on a server (like the Nethack and Crawl servers do) with a shared world, and finished games would be integrated into the history of the world. That could be interesting.
Something for the "someday" files. I'm satisfied with Nethack for now.