I wouldn't say the Ys games are similar... Darksiders is more similar I guess, but still not all that Zelda-like. But Ys is worth checking out, especially Seven and Oath of Felghana... not sure if Seven ever got a PC release though.
If you're willing to go for somewhat older console titles that are like Zelda, look into:
Alundra (Playstation): It's like a top-down view Zelda, but more challenging in every way. It's a bit more linear, but it's still a superb game with great music, great gameplay and a great story. For anyone that likes Zelda-type games, this is a must-play.
Illusion of Gaia (SNES): It's a lot like Zelda... more storydriven, I guess. But the gameplay holds up well too. You can increase your stats in this game by killing all enemies in a dungeon room, which is sometimes a puzzle in itself. Once you proceed you often won't be able to go back and the extra dungeon is kinda easily missed. I do recommend using a guide for the jewels since it's almost impossible to figure out all of their locations without one. The main game itself also has a couple of incredibly tough puzzles... the game itself came with a guide in the manual, so that says a lot.
Terranigma (SNES): A sequel to Illusion of Gaia. Entirely different setting & story & characters. A bit less heavy on the puzzle side and a bit more heavy on the action side. It never got a US release, so Japan & Europe only.
Lufia 2: Okay, it's not much like Zelda. But it's a fun RPG that has a crapload of puzzles... many good ones.
Read the mania: http://www.fanfiction.net/~nonexistinghero In SA2, it's Super Sonic and Hyper Shadow.
Dark Souls is like a much darker and unforgiving LoZ. Basically take Twilight Princess, turn off the happy parts of the plot, and do a three heart run with a blindfold and one hand behind your back to emulate the experience.
ADD, no. Where is the thread for Fallout OCD players? "We have to keep it on page 3 or it freaks out."
This is such a weird question, because Zelda has changed a lot over the years.
For 3D Zelda, I totally agree with the Darksiders 1 and 2, Dark Souls suggestions. There's also an old, old game called Blade of Darkness that sort of fits the bill, but you need to use joy-to-key to play with a controller.