I’m speaking for all the Italian Halo fans community (and I’m sorry in advance for any Written English errors), and I followed and commented Halos development since Halo 2 till now.
For the next saga of Halo, starting from Halo 4, me and most of the fans I represent would like to see:
-The return of the special relationship between Master Chief and Cortana, and a more emotional (and speaking) Master Chief. In Halo 3 he has lost a lot of “humanity” and seemed like a robot-that-kill’d-everything, a lot more then before. In Halo CE and Halo 2 he spoke a lot more, he had a lot more class and humor, especially with the Cortana’s word tricks. I would like him to return like that, even if war has changed both;
-A better told story and cinematics. Halo CE and Halo 2 were just amazing on how they told their story (even if I didn’t like playing the Arbiter and splitting the story arch in two), but Halo 3 missed something “deep” into it, and it feel like a bit rushed to the end. I would like to see a more cinematic and intriguing depth, like the books/novels, or movies. So: more cinematics, better dialogue between characters, and more twists and “climatic” moments well told;
-A more “Mature” look and feel of the Universe: many people are literally grown up since they started playing with Halo CE, from teenagers to Men. But even for the others I think it would be great to give Halo Universe a more mature color grading, realistic look and feel. Not only with the colors (less colorful, more “true”), but with a mature and deep world characterization, sounds, enemies, and every single aspect. I read Cryptum recently, and I imagined an Halo game with that feeling and depth, and, god, it would be so, so great if it will be like that;
-A more “optimized” and classier gameplay: with less confusing Armor Abilities for example. Giving the player all the same abilities for everyone like the previous game did, but leaving only abilities like Sprinting or Assassinate enemies, and that’s all. Invincible armors, invisibility, jetpacks…they were ok, but Halo must be the “perfect gameplay” and the perfect mix between: depth and easy controls. And have a lot of fun without thinking too much which “Perk” or “Class” must be chosen, and which is better or not;
-Big, open, explorable Environment: sandbox gameplay, sandbox exploration. Primary and secondary objectives. What Halo CE did in 2001, but a lot more complex and big at the end of 2012. Possibility to backtrack a level, explore and, in the same time, having action packed encounters like Halo 3/Reach. But not something like ODST. Only a big city or a big map, and that’s all. All levels must be unique, and different…but keeping the exploration and sandbox structure;
-Dedicated Servers for Multiplayer: while the Reach Matchmaking is the best P2P system ever made, it’s time to use official Dedicated Servers for every region (USA/Europe/Asia etc), for instant games search, lagless experience and to eliminate host power once and for all
That’s it for me.
Hope you guys from 343 will read this, and consider at least a bit of it. 
Thank You!