Kingdom Hearts 3 rumours (that is just rumors for you American readers) and speculation are found here. Please note this is not factual information, but purely guess-work. We have no way of knowing whether or not this is true yet.

By forum user Mr. Tinkerbell & Locke:

WHAT WE KNOW

The three armored characters that are shown in the “Sunset Horizons/The Gathering” and “Birth by Sleep” secret trailers ARE NOT Sora, Riku, and Kairi. Similarly, the bald man is not Ansem/Xehanort or his Nobody/Heartless.
The names of the armoured characters are: Ven, the Roxas-like character who is frozen; Aqua, the knight with blue hair; and Terra, the largest of the knights and the one who’s face is revealed at the very end.
The Enigmatic Solider is, in fact, Terra, and is hinted to have some connection with Xehanort, though what that connection is, is current unknown. An interesting trend between them now is that they both look similar, and are ‘Enigmatic’ secret bosses.
There are a lot of keyblades, a war is coming or has passed.
The Crossroads are important.
Has something to do with the Keyblade bringing chaos.

DENIED RUMORS
As hinted by Nomura, the story WILL NOT revolve around Sora, as he wants to leave Sora ‘on a break’ for now.
THERE HAS BEEN NO CONFIRMED BOX ART. The box art you see online bearing the name “Kingdom Hearts III” is not the real box art, as there are several flaws - there is no subtitle for Kingdom Hearts III and the side of the box actually has “Kingdom Hearts II” as it’s logo.
The next game will not be titled Kingdom Hearts 3.
The next game will not be on the Playstation 2, as Nomura has stated his last game for the PS2 was Final Mix +.

WHAT WE DON’T KNOW

Who the distant outlined figure is.
The place in the Kingdom Hearts timeline this trailer takes place in.
What the text means by “birth by sleep”.

These worlds are based on my own assumptions and predictions, they are to be considered rumors.

Kingdom Hearts III will continue to feature Disney related worlds since that is the main aspect of the game. Due to some new ownership and popular previous worlds, many new and old worlds will likely make a return.

Pixar Worlds

Pixar worlds are an absolute in Kingdom Hearts III. Previously, modern-classics like “Finding Nemo” and “Toy Story” were not featured in Kingdom Hearts because, despite the Disney name, were registered with Pixar, a seperate company. But since the development of Kingdom Hearts II, Disney finally bought Pixar. As a result, all Pixar characters and movies are under the Disney Empire and due to their critical and commercial success, it would be a missed opportunity not to have these characters featured in the next game.

Toy Story - “Andy and/or Sid’s Room”

With new ownership over Pixar, we may see a new level where Sora and Co. are the size of toys, much like when you shrink in Wonderland in the first game.

The Incredibles - “Nomanisan Island”

Everyone remembers the secretly evil island from the Incredibles where the super-family spring back into action to take down the nasty Syndrome. It wouldn’t be a long shot to say that Sora, Donald and Goofy might don some tights and help the family out in the next game.

The Hunchback of Notre Dame

A world and characters that were heavily requested in Kingdom Hearts II but never made the cut. We may expect some appearances in the next game.

“100 Acre Wood”

The one world in both Kingdom Hearts and Kingdom Hearts II where no Heartless roam. In this world the player simply plays through simple mini-games. This has proved to be popular, especially since it is completely optional and provides a good game for younger players. Since it came back in KH2, it’s likely it will come back once again.

“Olympus Colisseum”

The tournaments on the Olympus world have been favorites of fans since the first KH game. Being one of the most visited world in any of the games, it would be unheard of to exclude it from the next game.

New World - “Sand World”

The world visible in the Secret Trailer at the end of Kingdom Hearts II may be a world in the next title, considering the World That Never Was from Kingdom Hearts II was featured in the Secret Trailer from the first Kingdom Hearts.

“Hollow Bastion/Radiant Garden”

Being the very most important world in both Kingdom Hearts and Kingdom Hearts II, being the root of all evil and good, it’s quite likely that it will play another large part in the next game. Probably being the world that is safe to return to at any time full of shops like Traverse Town or Twilight Town.

“Destiny Islands”

Since this is where the characters were last left off, it’s almost impossible for the game to not begin here. And with the game likely being on Playstation 3, it’s an excellent place to present the amazing new graphics. A world full of palm trees, sand, water, a nice sunset/rise and a quite little village.