Oh, you already mentioned Soleil.
Maybe
Legend of Thor (Genesis) too? I didn't play it yet, it's on my backlog, so maybe I'm wrong here.
I agree with Okami, for the alternate map/dungeon, but with less key/item/boss finding per dungeon. Great game, even if the intro could seems boring and too long. One hour intro is nothing when the game need 100Hours for 100%

I didn't know Darksiders was considered Zelda-like. I'll have to try it.
I wouldn't consider Faxanadu as a Zelda game, it's more a Metroidvania than a Zelda.
Mystic quest for GameBoy is actually Seiken Densetsu 1 (Secret of Mana series!), remade as Sword of Mana on GBA. nothing to do with Zelda (except dungeon exploration? and the per-screen area scrolling. But it's more RPG to me, as long as you gain Exp/levels)
Full Zelda genre clone, I can only think about
3D Dot Game Heroes on PS3, which is a Zelda 1 Clone/parody/homage? Very good game and nice dungeons.
I'm sure I played more Zelda-esque games (alternate outside world/dungeon/item/upgrades), but I can't remember them right now.
Edit:
Damn, I forgot to list Alundra 1 (PSX)
Mystical Ninja starring Goemon (N64)
There are derivate genre, users could think it has nothing like a Zelda game, but you might want to give it a try:
- 3D Isometric:
LandStalker, (Genesis), which is a good game.
Lady Stalker too, but I never could play it more than few minutes, not as good as LandStalker.
Maybe Light Crusader too? but controls seems awful.
- dungeon-only games : Solstice (NES), Equinox (SNES).
- Action-Adventure-only games: Illusion of Gaia (Snes), Terranigma (Snes). they are without a main map with multiple dungeons, you only follow the story.