DarkSiders, Metroid Prime, Kingdom Hearts.

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You're looking for an action-adventure game, not an RPG. Very different genres.
As for adventure games that have a similar dungeon and puzzle focus, I can name three excellent ones off the top of my head:

1. Okami: The closest you'll get to a Zelda game. It's directly copying the formula used in OoT. You can find it on the Wii.
2. Beyond Good and Evil: It's not as close to it as Okami, but the resemblances in storytelling and dungeons are there. Gamecube title.
3. Darksiders: A bit darker than Zelda games usually are. A sequel is coming to the Wii U.

There are also a dozen I can point to that use the 2D Zelda style, but if you're looking for 3D start with those.

People keep telling me 3D Dot Game Heroes and Gurumin are like Zelda games. Never played them to know.

You could try the Metroid Prime series, It's an awesome adventure series, but if you are playing them for your first time, meh, you will get lost, you could also try Banjo-Kazooie or Banjo-Tooie, Conker's bad fur day, or try to get a copy of Skyward Sword, It's really worth every penny. And like people above me say, Okami, I have not played it myself, but people say the game is very Zelda-esque and the music is beatiful.

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Banjo Kazooie and Tooie, great games

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There is no game that is like Ocarina of time! ocarina of time is one of a kind game!!!

but there are some games on the same idea like Banjo kazooie

One does not simply make a game similar to a Zelda game.

when I was a kid I went to a store with this same question, and this is what they told me to get:

Mystical Ninja - Starring Goemon intro - YouTube

even if the fighting and puzzles are kind of like Zelda, the game is epic on its own and deserves a 3DS remake.

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Not really.

I can only think of the freedom you are given(and by "freedom" I mean the just roaming around an accompolishing nothing aspect) as a similariy.

Zelda OoT is an action game with very few platforming elements(poorly designed ones at that) with focus more on combat and weapons.

While Banjo Kazooie is a 3d platforming collect-a-thon(jiggies, jinjos, musical notes, honeycomb pieces) which has a very little focus on combat at all(yes there are some cool moves you learn as you progress, but really, shooting eggs and your basic tutorial moves are all you need).

As for OoT. Twilight Princess is basicaly that with Wolves.

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Thank you for recommending Darksiders. I'm totally downloading this one for PC.