I would like to see the next Zelda become more serious then all of its predecessors. Don't get me wrong, I don't want a GTA version of Zelda, but I immensly enjoyed Zelda Twilight Princess because it took a more serious approach to the game. I think more adults play Zelda then kids. I wish Nintendo would reflect that in the next game.

Smarter and more varied enemies and bosses that are more intense but not larger then life.
Multiple difficulty settings
Item weapons should be able to string into a combo (like Batman:AA)
A game that moves forward with no need to go back to an already beaten dungeon.
I want more character development through side quests.
A darker more political take on the story with more countries/races actively involved in the fight against Ganon
More cinematic sequences (like Uncharted)
Voice acting in every character except link with the option to toggle voice acting if unbearable

edit:Oh and I've always wanted a Zelda in a futuristic fantasy setting. It worked for Final fantasy why not Zelda?

We won't be getting a top-down console Zelda game as long as Aonuma has something to say about it, but I'm fine with settling for the next best thing, which is everything in this post. Plus...

1) Ditch the boss intros.

I could seriously dig that second Ghirahim fight if the sonofabitch just lunged at you instead of monologuing for several minutes. Building up some tension before the final boss I can understand, but enemies like Volvagia should just shoot out of the ground and start breathing fire at you the millisecond you enter the room.

2) Only a short intro before you can access the overworld.

Just a skippable cutscene that triggers after a while of not pressing anything in the title screen would be enough for me.

3) More enemies in the overworld.

4) Give me back my Koji Kondo and Toru Minegishi!

Hell, just Minegishi is good enough for me. Kondo seems to be kind of losing it. In all the other Zelda games I've played, (and even Majora's Mask, which I haven't) there are at least five (though usually more than ten) tunes that I might just spontaneously start whistling as I go about my day. In Skyward Sword, there are two. And one of them is just Zelda's Lullaby played backwards.

I like fast, melodic, invigorating music, so Minegishi is pretty much my favorite video game musician who hasn't worked for Capcom at one point or another.

5) Maybe set in the Adult Timeline, right before the deluge?

I'm not sure about this one, since we all already know how it would end, but it would certainly be interesting.

Yeah, mostly just recycled Malstromisms, but hey, that really is what I want.

1.) Change the music.

The music in Skyward Sword was not memorable at all, and I consider the tunes the major highlights of the Zelda series.

2.) Do not remind what each item is after I already picked it up.
This was my biggest gripe in the game because I had to read all the descriptions when I turned my Wii off the last time

3.) Voice actors for everyone except Link.
I was able to live without it in the other Zeldas but it is pretty much necessary at this point. Especially when the dialogue has to be forcefully read through anyways, they might as well say something.

4.) Darker Zelda please.
Twilight Princess had flaws but I enjoyed that games environment more than I do the one in SS. Everything is bright and colorful, so it doesn't seem like the world is really in the peril that you assume it should be in. Factor in the tame music and well, the game isn't very serious.
Majoras Mask had the giant MOON looming down on you and time working against you. Ocarina had the entire town, destroyed with seriously creepy ReDeads roaming around. SS gets real close to Kirby's Epic Yarn in that regard.

5.)Shorter introduction
You shouldn't have to play 5 hours or more before you get to kill something; prevents people with less patience (if the series is new to them) from buying it based on word of mouth.

6.) Bring back the battles moves from TP that you learn over the course of the game.
7.) More enemies please...there are only like 10.

I'll echo some of the sentiments expressed here. Pardon my inability to properly elaborate, because it's currently 8:00 AM in Japan and i have to go to study abroad orientation soon...

I'll go off of what we were presented with Skyward Sword, because i loved a lot of the changes in Skyward Sword, and add the following:

1. Overworld should feel more lived in. It's something that's a little tougher to balance out, but i like finding little villages and things here and there all over the place like in OoT, even Twilight Princess for all its sprawling overworld had the problem of little to no civilization (though the bigger problem was that there was little to no nothing in that overworld). I very much enjoyed Skyward Sword's creation of depth and challenge in the overworld, but the layout should feel more organic (which also means: no more dividing worlds up arbitrarily a la Metroid Prime 2 or 3, and yes i'm aware i just said Metroid).

2. Deeper weapons upgrading, namely with the inclusion of swords.

3. Slightly more aggressive enemies. Yes, it would be nice to be attacked unprovoked once in a while

Yeah, figuring things out has always been the main point of the game.  I always have enjoyed the puzzles in Zelda since it makes the game more about using your brain and less about how dextrous your thumbs are.  At least that's my two cents.

* No Cel Shading: Not because I hate Cel Shading, but for me, it simply doesn't fit Zelda. Zelda was always "dark" and "serious" (Link's uncle who dies in ALTTP, the dark world, the cursed Deku Tree in OoT, the starving Gorons, Hyrule ruled by Ganondorf with the zombies, and many, many more in OoT, the the moon in MM with the time limit (And yes, I think that the time limit was a GREAT idea), et cetera. Maybe I interpret a bit too much in some of the older games, but I don't want the next Zelda to be a "funny" Zelda like Wind Waker or (to a certain decree) Skyward Sword. This DOESN'T mean that Nintendo should make the graphics anything close to realistic, I just want a more serious Zelda game. WAY more serious, even at his "death" scenes. Hell, when I was playing Skyward Sword, one of my parents started to laugh because of Links sound he made. FYI: Link fell into the lava.

* Better controls: The motion controls of SS were good, but nothing more. They were responsive (maybe sometimes a bit too much), but the whole "recalibrating" EVERY time you point out of the TV range with EVERY item was hella annoying. Also, I wish it would be for me (as a player) to decide when I use the motion controls of an item, since it wasn't even possible to focus at an enemy, because it always switched the perspective when I used an item like the bow.

* More (important) areas: Skyward Sword had... what? Skyloft, a forest, a volcano, a desert, and some minor areas like the bamboo isle or the isle of the songs (is it called like this in the english version?)

* A GOOD overworld / world map: Skyward Sword did pretty much the same as Wind Waker... But even worse. One of my major complains about the world map of WW was that there was... pretty much nothing to do. There were some treasures you could find, a few small islands, but... that was pretty much it. SS had even less to do. I wish they'd just make it smaller, but with WAY more content. Minigames, sidequests, heart pieces, treasure chests or something else.

* More, better and BIGGER dungeons with more puzzles: What I REALLY loved about the old Zelda games were the (sometimes) HUGE dungeons like the Fire and Spirit Temple with loads of puzzles where people really had to THINK about how to reach a certain spot or (in OoTs case) how to reach a Skulltula / whatever. SS's dungeons were ridiculously small compared to that and the puzzles were WAY too easy.

* Don't add crap that don't fit to Zelda. When I saw the train in Spirit Tracks, I was like "What the fuck are they doing?" and now, in Skyward Sword... Robots? Really? I mean, Zelda always had a few (more) modern elements and even a few robots like the Beamos, but I honestly couldn't care less about robots as a race >_> Really Nintendo, give me back my medieval (ONLY) Zelda! D:

* Don't restrict me / my gameplay experience in ANY way. I was really excited when Nintendo said that there's time traveling in SS, but ultimatily, it was the same crap as visiting Hyrule in Wind Waker. The only thing you could do after you traveled back in time was planting a stupid tree and fight at the outside. Nintendo could've easily doubled the content with something like this.

* No safe points. I want to save whenever and wherever I want.

* Try harder with the NPCs: Do it like MM, where most NPCs had a personality, a background story and a sidequest, not like this "demon wants item" bullshit, but something like the Anju and Kafei sidequest.

* Music: Give me back an instrument where I can play (like the ocarina of time / fairy ocarina and the wind waker) and has real music (but "full" songs like OoT/MM and not like the wind waker), not crap like the the lyra and let me use the songs for quests, dungeons, et cetera. What I liked about OoT/MMs songs was that they weren't just used once for opening something, but used during the whole game. Regarding BGM, I wish for more "dramatic" BGMs, e.g. when I fight a (mini)boss. Remember Majora's Mask when Link entered this jukebox-like house and you saw Pamela's father as a Gibdo? THAT's what I want to hear. THAT's what I consider great / damn near perfect boss music. Skyward Swords miniboss battle music was extremely boring, to be honest... no, the whole music in SS was pretty boring and not memorable at all. Even with the 5 songs you learn for the lyra, only 1 of memorable (Well duh, guess what song) and only 1 other was even remotely GOOD (Nayru's wisdom)

* Give me back some day and night cyclus, preferable like MM, but AT LEAST something like OoT, where some minigames and side quests can only be done at certain times and where NPCs were different / only available at certain times. Seriously, in SS, you couldn't even FLY at night... It's as if Nintendo wasn't even trying...

* A helpful sidekick: Phai (Or Fi in english, afaik) was great. The only thing that could have been done better about her: Give me USEFUL tips ONLY. I couldn't care less about useless information like "Ghirahim calls himself Demon Lord blablabla", and if I ask about infos about an enemy, I ask about infos about an enemy ONLY. No information about equipment, balance, time, whatever. Just about what I'm asking. If she doesn't have informations for me and if I have to click the A button like a hundred time to quit the dialogue, then there's something wrong with it.

* Give me an antagonist from the very start. Sure Ghirahim was always about "freeing his master" and whatever, but Demise appeared... what, in the last 5 minutes of the game? (And I'm not talking about his other form)

* Obviously, no voice overs, but make the NPCs look and sound less stupid. When I saw and heard this guy at this bamboo island for example, I honestly thought he was gay... Please no characters (design-wise) like Beedle, Bertie, Fledge and this boy with the pineapple head or crap like Ooccoo... >_>

* Add some nostalgic elements: What I'd really like to see would be elements from older games that have nothing to do with the gameplay or story, for example, I'd really love to hear the shop / basar music from OoT in newer Zelda games too. But that'd be just a small extra.

And last but not least:
Remove the GODDAMN stamina bar. Seriously. I hate this bullshit. If Nintendo gives Link the ability to run/swim/climb/whatever, he should be able to do it all the time without interruption.

My post probably has some(?) nostalgia in it, but ultimatily, this is what I want. A darker and more serious Zelda with bigger and better dungeons and better overworld with more focus on NPCs, better and more memorable music and less useless crap / more useful game elements.

Now that I've had a bit more time to think about it, I'd also like for there to be less of a tutorial section. I'm not saying we need to be thrown into the deep end no matter what, I'm just saying we should get a sword early on. We should be made to learn the emergent function of the games in the order of their importance. Fer instance, sword should be first. After that we might could get a shield, maybe! It depends. Travel should come afterward.

Zelda is one of the best games in the business when it comes to emergent gameplay, and I'd like that to be more of a tight focus in the next game, even if it means that early on the story has to suffer a bit.

I think Zelda would be better served following more of the Oblivion/Skyrim blueprint, as in, more open-world, exploration focused. If you look back to the original Zelda on NES, and even Link to the Past and OOT somewhat, they are more in this style, and I think that's what the spirit of the series should remain. Zelda nowadays is becoming far too linear, more slow paced, and chatty NPCs.

I'd argue that this was never really the case. Yes, you could go about the overworld as you liked in the first game (not in subsequent ones), but progression still required the abilities that emerged as you gained items, and the gaining of those items was often very linear withotu some serious lateral thinking.