For complete api documentation visit ApiDocumentation
For the official javascript client library documentation visit JavascriptClientApiDocumentation
(These are not officially supported or tested, but might still be useful.)
ActionScript3
http://github.com/julien/as3_bitly
C#
http://sites.google.com/site/bitlyapp/
http://code.google.com/p/bitly-dot-net/
Java
http://code.google.com/p/bitlyj/
http://github.com/finnjohnsen/BitlyAndroid
JSP
http://www.servletsuite.com/servlets/bitlytag.htm
javascript - jQuery
http://code.google.com/p/bitly/
PHP
http://github.com/Falicon/BitlyPHP
http://blog.verkoyen.eu/blog/p/detail/bit-ly-php-wrapper-class
http://classes.verkoyen.eu/bitly/
http://www.yiiframework.com/extension/bitly-url-shortener/ (yii framework)
Python
Official Python Client http://github.com/bitly/bitly-api-python
http://opie4624.github.com/bitly.py/
(for Google App Engine) http://www.chrishannam.co.uk/2009/01/bitly-competition-entry/
http://code.google.com/p/python-bitly/
Ruby
http://github.com/nas/url_shortener
http://github.com/playgood/get_shorty A ruby gem that extends ActiveRecord models to cache a short url from
http://github.com/philnash/bitly or "sudo gem install philnash-bitly"
https://gist.github.com/843371
VB .NET
http://www.databatrix.com/2009/08/a-net-bit-ly-api-helper-class-visual-basic-net/
http://bitly3.codeplex.com/