Idea #1: Rogue Like Hell (or, "Roguelike your Life Depended on It").
The dungeon is dark. The monsters are deadly. WAY TOO DEADLY. You are not a hero. You're a lost fool with a scant few tricks, running for your life amid the horrors, hoping to find the light. You have no aspirations of glory. The day is too dark, the monsters too vicious. You might, might slay a scant few of them in desparation, but clearing dungeon levels is out of the question. Your tools are more focused on stealth and tactical manipulation (shoving enemies, tripping them, short-range teleport of self and others, closing and locking doors behind you, etc.). Basically, you spend the entire game on the run from overwhelming forces at your heels, trying to eke out just enough advantage to stay ahead of the hordes of darkness.
Idea #2: Dungeon Sabateur
This idea is based on an old DOS game I played back in the day, called Pyro 2. It consisted of randomly-generated levels representing floors in buildings you were supposed to destroy. Scattered around each level were various gas canisters, which would start spreading out as you walked past them. The player trailed a lit fuse behind, and you had to try to set off as big a fire as possible without burning yourself alive. The original game certainly had important roguelike aspects -- random level generation and permadeath -- but I think there's room for a re-exploration of these ideas in fun new destructive ways (molotov cocktails, anyone?).