Where can I find a central repository of all available Arduino libraries?
Since this question was first asked, there is now the Arduino Library Manager, built into the Arduino IDE. There you can search for and install libraries.

There is information about how the library manager works here:
https://github.com/arduino/Arduino/wiki/Library-Manager-FAQ

There isn't however an official website listing the libraries, so I recently created this unofficial site, based on the same data in the Arduino Library Manager:

http://www.arduinolibraries.info/