Java Edition Infdev
You must buy the game in order to play infdev.
Infdev is a mode still under development, available only to those who have bought the game. Its main feature is generating maps of incredible size (8 times larger than the surface of the Earth, according to Notch). Currently, it generates strange landforms, including floating islands and strange looking cliffs that do not form normally in InDev. If you die, you can respawn at your starting point, but you drop all the items you were carrying (you can pick them up again if you can reach your body before the items expire).
It's a good idea to build a base directly over your spawn point, making sure not to obstruct it.
Mobs and more realistic trees have been added on April 15th, 2010. Few more key features from Indev haven't yet been added, although Notch intends to re-add everything in upcoming updates.
InfDev replacing InDev
Sometime in the future, Indev will be replaced by Infdev. It is speculated that all original Indev maps will be able to be loaded into the new version.
For those who like InDev and don't like InfDev fear not. It has been confirmed that while InfDev will replace InDev as the main focus of Minecraft post-beta, smaller maps will still be available for those with less powerful computers or who just like the "less to worry about" atmosphere of current InDev style maps (reference)