I'll add Angband to the list. A hack-and-slash roguelike. 1 town, 100 dungeon levels, kill Morgoth and win the game. Diablo 1 was heavily inspired by this game (and Moria).
Artifacts, ego types, and most normal objects have to pass a depth check before being generated. But nothing in the game has a depth below 100, so there would be no difference between 100 and 200 from that perspective.
It might be easier to find weapons with higher +to_hit and +to_dam values, or armor with higher +ac, but that would be unlikely to matter much, because you'd be using artifacts anyway.
I don't know if rings of speed take dungeon depth into account. Most other types of bonuses in the game are capped. (e.g. a Ring of Constitution +6 is as good as Rings of Constitution get.)
Angband is great, and was great to find after having played Moria on and off for a few years. The game that really caught me was one of its variants — Zangband. Not because of the Zelazny connections, but because of the sheer size of the gameworld and everything that could be found in it. It hasn't, however, apparently been updated since the mid-aughts.
Dungeon level 100 doesn't have stairs down, but you can get to level 101 by falling through a trap door on level 100.