I would like a Zelda game where you can also play as Zelda, just for a change, maybe use some magical powers? I like the idea of a few low tech gadgets as well.
Sword play should still be the main element but it should be far more challanging then in TP, where it was simply far to easy. Puzzle elements should ofcourse be kept, but maybe it's time to scrap the temples.

I think Nintendo will do exactly what it wants to do. After doing something as ground breaking as WiiFit I can't see them backing away from changing a game formula.

Whatever they decide to do with the next console-Zelda I think they should keep up with a few things:

1. Koji Kondo's music. I can't imagine a Zelda without those haunting sounds.

2. Many Side-quests (TwilightPrincess was a bit dissapointing on that... Remember how FULLY LOADED with sidequests the Windfall Island was in WindWaker... night-time auctions, spying, photo-shooting...). In my opinion these SideQuests offer as much excitement as the Temples (and sometimes even more... remember the Scultulla hunting at Ocarina, especially at nights with the scratching sounds... ).

3. A VERY interactive Village (Kakariko-style). Again TwilightPrincess suffered from that. Kakariko was barebones, not much to explore and do. Give us many shops (open at different hours), with more mini-games and a reason to collect all these ruppes... (at TwilightPrincess we had tons of ruppes at the end with no use)

4. The Hookshot. It's the ultimate Zelda weapon. (I don't care about the Ice/Fire/Light arrows, but the Hookshot is a MUST).

5. Fairy in a bottle. Again, this is a Zelda trademark that needs to be there no matter what! 

*** As for the Art-Direction, I think Nintendo needs to trust in their own insticts and artists, and not try to make a 'Lord of the Rings' universe (this is how Twilight Princess smelled here and there...).

Any other suggestions?

nintendo need to give something to the hardcore, and Im not talking about super mario sluggers, because if they dont show much if any hardcore titles this E3, they have officialy gone casual.

I'd love some JRPG influences in the next Zelda, especially the FF4 industrial age theme is something I really would like to see.
Also a more complicated storyline and indeed the WindWaker-type sidequests would be much appreciated.

Couldn't agree more with you guys! Wind Waker's style is unbeatable!!! 

I think Nintendo's latest attempt to bring a Lord of the Rings 'spikey' touch is not necesary at all. The colours were muted and there was a foggy quality all over the world. 

The artistry of Wind Waker is the highest they ever achieved. At least for my taste.

Things I'd Like to see in the next Zelda:

1)Many Zeldas have two different worlds (OoT: Past/Future ALttP: Light/Dark TP: Hyrule/Twilight). For the new, I would like to see the same mechanic just wildly stylized. Light and Dark are old, lets bring the Zelda worlds together Classic Hyrule/Cel-shaded Underwater Hyrule. Or make one world Steampunk or water-based technology and make the other Solar or fire-based technology. Just do something interesting with the two worlds.

2)Items - new items are a must. I cant tell you the feeling I had when I picked up the Ball and Chain in TP, it was great! In addition the Items need to be upgradable, not just the sword. I do like sidequests to be the way upgrading is done.

3)Story. New villian.

4)Characters. Make many different character trees and make dynamic relationships that effect story development.

I personally hope that it's different. I know that some people won't like this but I didn't that Twilight Princess was that good at all. It didn't take any chances. There was nothing new about it. When they say that it will be different I hope that doesn't mean a "casual " game though.

Buy the GC Zelda Collector's edition already.  A little more than buying each one on VC, but well worth it.

Forogot more than Majora's Mask.  Where are Oracle of Ages/Oracle of Time, and Four Swords Adventure?

Man obviously.  Zelda changes into Sheik through magic so it's not like it's a simple change of clothes.