Though very little information has been spread concerning Final Fantasy 13, we do know a few tidbits about it. Below is a list of what we know, and is subject to change as we learn more.
Exlusive to the Playstation 3.
The crystal will play some part in all three games, as suggested by the compilation's title: Fabula Nova Crystallis ("The new story of the crystal.")
Futuristic style (guns, explosions, trains...).
Probably a new battle system, though ATB seems to play a role.
Made by the same guys as Final Fantasy 10.
All 3 games will have their own storylines, characters and worlds, yet will retain some form of continuity.
The main storyline for the compilation will revolve around the crystal, and it "leading the world towards the future". Crystals will also be commonly found objects.
Moogles and Chocobos will return!
The main character of Versus (the KH-team-created title) is a member of the royal family. This family has protected the crystal for generations, and this main character is no exception.
Agito will take place in some sort of school, involving 12 kids who wield different weapons.