Imagine a world of possibility. A Minecraft where your world is the only one like it. A truly unique experience each game. This is what I am offering to you.
I will provide this dream to you in three sections, to make life easier!

Section I - An infinite world height.

Envision a world where you can dig a mile in to the ground or build a mile in to the sky. True potential to create anything that you can fathom.
This is not a real possibility in the current game of Minecraft. This issue has been brought forward a great many times by people who suggest we should raise the height limit. This will not work. For starters, the game will lag. A lot. You are effectively doubling the amount of blocks that need to be rendered at any one time. Others suggest we simply make a chunk infinite vertically. This will, obviously, not work. You'd be lucky to have half a computer left when you're done trying to load that.

The solution is more simple than you would think though. A three dimensional chunk axis. It has been suggested in the past but never implemented in a fully functional form. The concept is simple. Our world is built upon a grid of 16x16 chunks, so why can't we have these chunks stack as well? A cubic world of 16x16 squares coming together.
Any height.
Any depth.

Of course, this won't come without problems. Ore spawning would need to be tweaked. If you had to dig 15 million blocks down to find diamonds near the bottom of the map, there would be rage. It would be possible to layer the world, however. Have diamonds occur on a certain chunk, then repeat, like a pattern.
There is also an issue raised that comes to lighting, which is currently rendered on a chunk by chunk basis. This could be combated by implementing a dynamic lighting system that processes lighting globally based on the position of a point on the Minecraft sun and moon.
It would be quite difficult to fix these issues, but not impossible. Let's say we do fix them. What comes next?

More worlds to explore. Something beyond the overworld, Nether, and End. Perhaps even different worlds on the same map. Dig far enough down and you reach the nether. Even further and you get to the end! If you could up you could find the Aether, much like the classic mod. Even higher and you find space. New creatures depending on your height level in the world.
A whole new universe.

Here's a sample of what the cross-section of a Minecraft 2.0 world could look like. Picture is not to scale.


Section II - Custom generated structures

Do you dream of a world that has more structures to explore in-game? A world with more NPC's and liveliness? Are you one of the people who has begged Mojang for better buildings for years? Why wait? I envision a custom building creator, a unique map option that allows you to build different structures and save them as custom buildings that will appear on your Minecraft worlds.
Do you want villages to have walls and watchtowers? Then go ahead and build it! Just save them as a part of a village folder and bam! You have customized villages.
Now let's say you want to make your own dungeons, something crazy, big, expansive. That can be a reality. Simply build each room you want to appear and select an option that will piece them together underground!
New Mineshafts!
Custom castles!
Cities floating in the sky!
Whatever you can think up in your mind can become a part of your world! This idea would take some serious programming and would require a new structure generation API, but it's definitely possible.
These structures could even become a part of resource packs, their generation easily enabled and disabled. (If you disable the structures on a map that had them enabled before, they simply won't generate on new chunks)

Section III - Friends and social interaction

In the previous section I told you about how you could build your own custom structures and have them appear in game. But what if you want to share these buildings with your friends or check out theirs without having a go to a site to download the schematics? Imagine being able to do this in game.
Right now, the closest thing we have to a social networking system IN Minecraft is Realms. And Realms is overpriced trash. I propose a new feature, one that lets you add other people to a friends list and shows you what server they are playing and vice versa. The ability to invite friends to your games or worlds.
Additionally, you could link your PlanetMinecraft and MinecraftForum accounts to this service, and automatically upload anything you want to share for people to see and download!
This idea, for a social system, would be the hardest to implement in to the game. This would require millions of dollars in to investment for servers and a hosting system that can link a game to website. But, it's not impossible. A large chunk of the required server space could be acquired from the Minecraft Realms servers. This would mean Mojang would need to stop Realms, but let's face it, only around 10 of the 100 million PC Minecraft players actually use it.

Conclusion

These ideas may seem to be very different and far apart from each other, but combined they would form a web of game changing features that would make game-play completely new but still keep the original spirit of Minecraft intact. The freedom of the human mind.