Alundra was better than Zelda at the time of its release.

Absolutely Alundra, can't think of another Game that is Like zelda

This!!! 

Star Fox Adventures could count as one, no?

This should have been on the poll. First game I thought of when I read the post's title.

Darksiders. I wanted to love Okami but found the game to be ok. That was mostly driven by the non stop talking. The game is stunning and has amazing art style, and was disjointed by characters who never STFU. For the most part nothing rivals Zelda, except Souls.

Okami without question. I think it's better than even most of the Zelda games too. For more old-school style 3D Dot Game Heroes is excellent, and more people should play it.

3D Dot Game Heroes is by far the best, but Blossom Tales was pretty incredible especially for the price. I wanted to enjoy Okami after the rave reviews, but got a few hours into on the PS3 before moving on from it. Might have to give it another try one of these days, but I wasn't impressed with it.

I have played about half the games in the poll, and I don't like any of the ones I tried.  To me the best game that captures the Zelda spirit is:

Adventure (Atari 2600).

There really aren't many games that are both good and give me the same feel from a good Zelda game.  Here are a few that are reasonably close:

Wonder Boy in Monster World
Adventure Time: Hey Ice King, Why'd You Steal Our Garbage
Adventure Time: The Secret of the Nameless Kingdom
Dark Souls
Minecraft

Breath of the Wild