Note: while this post was originally made by nexy it has been highly edited since.
What is Raspbian?
The short answer is "It's an unofficial version (‘port’) of the upcoming ‘wheezy’ Debian Linux that is optimised for the Raspberry Pi."
Debian offers two arm ports. The "armel" port will run on the Pi but it doesn't take advantage of some of the features of Raspberry Pi's processor. In particular it does not make any use of the floating point support in the Pi's processor making code that uses floating point heavily very slow. The new debian "armhf" port requires features that the Raspberry Pi's processor doesn't have. Raspbian uses the features the Raspberry Pi does have, but doesn't use the features that are missing.
Technical differences between Raspian and the Raspbery Pi Foundation's Debian port mean some programs will experience a very noticeable performance improvement on Raspian. A bigger and better explanation, along with a more technical details for those who want them, can be found on the Raspbian FAQ page.
Who is Raspbian for?
Raspbian is now the reccomended distribution for most users of the raspberry Pi. The exception being users who are dependent on software that is not yet present or functional in raspbian.
What is this sub-forum for?
This forum is primeraly for Raspbian specific discussion. Having said that if you are not sure if an issue is Raspbian specific PLEASE raise it here first before taking it up with upstream.
Kernel issues (if it crashes the whole system it's most likely a kernel issue) are probably better taken up in the "linux kernel" forum here. Note that Pi kernels are heavily patched so unless you are absoloutely certain it's not a Pi specific issue (e.g you can reproduce the issue on non-pi hardware) please don't bother upstream about it.
What's already in here?
Debian Hard Float (armhf) for RPi - Large thread chronicling mpthompson's amazing work with plugwash and others to bring Raspian to life.
Port of MATE to Raspbian. - MATE is a fork of the Gnome 2 desktop environment.
Donations for Raspbian - The project has cost about $3000 to Mike "mpthompson" Thompson personally already. Understandably donations would be gratefully received to help further development.
Where else should I look for Raspian information?
The first place to look is the official Raspian homepage.
For more history, there's mpthompson (Mike Thompson)'s posts on the Debian arm mailing list.
And mpthompson's original forum thread about what would later become Raspian.
Where can I get it to try?
After you've read the Raspbian FAQ page, head to the Images page and select from one of the images available. We reccomend that begginers use the Foundation image
For more information
Please visit the official "Start Here" page on the Raspbian wiki.