For me it has got to be the next 2D Zelda. I'd like it to be less like the DS ones and something closer to Four Swords Adventures but with the focus being on single player. The last game that truly fit that for me was probably Minish Cap.
Confirmed or not, Metroid Prime 4 isn't one of my most-anticipated games.
I don't really have anything specific in mind I'd like to see, but in general, I like to see wild new ideas (Splatoon) or sequels that try some new ideas with established formulas (Super Mario Odyssey, it looks like).
From Nintendo specifically? Probably a new F-Zero game. Or the return of Advance Wars! Wouldn't mind a sequel to Code Name: S.T.E.A.M. as well. Or some kind of new IP, obviously.
A game *not* from Nintendo? I'm game for whatever Capcom is doing next with the Resident Evil series. (besides the RE2 remake) The Revelations "series" was good, and I've heard nothing but great stuff about Resident Evil VII. Keep it comin', Capcom you're on a roll!
The last game that truly fit that for me was probably Minish Cap.
If we're talking about projects that are all but confirmed I think I'll have to say 2D Zelda too, for the same reasons. EDIT: Damn, I forgot about Link Between Worlds! How could I? Well, it doesn't change my answer as such, just the reasons a little bit.
A somewhat plausible dream would be a new Fatal Frame game, 'cause they've been high quality scare fests, even if the latest game dropped the ball with the pacing.
As for ridiculous wishes that will never come true, I'd love to see the old Cing staff close the book on the Kyle Hyde/Ashley Mizuki Robbins stories.
Unless a full, real, ACTUAL sequel to the real, original Chibi Robo came out (and at this point, I think it's only in my dreams) I agree with @DrFinkelstein it is for sure Animal Crossing. I have such high hopes after New Leaf. I hope they really go all out. What I'd LOVE is if they made it a little more "open" feeling like:
Imagine if you could run around that and even jump and stuff, it could be so much fun. And compare that to the starkness and "grounded, plain" feeling of:
Just can't compare. I am hopeful, but even if it isn't a huge leap forward for the series, I will still play and love it I'm sure. :)
I feel like an Advance Wars with GOOD online (shouldn't be hard since it isn't real time so they mostly just have to focus on the modes / user experience, etc.) would be so awesome. Imagine for instance if it allowed like up to 8 players or something and you could do like 2 teams of 4, or 4 teams of 2, or 8 players everyone for themselves?! Not sure how it would handle disconnects, maybe just replace the player with a bot if that happens so as to not destroy the whole experience?
Even better would be if it had an asyncronous mode so people could play against each other without having to be sitting right there with the thing turned on. Maybe they could set turn limits... 4 or 12 or 24 hours or whatever.
The next Kid Icarus game. Though who knows what that'll be like since Sakurai probably won't be working on it. Then again he's been doing Smash and keeps saying he's done with it... so maybe he will Uprising was just so damn good.