Quotes Database System (formerly Salty Quotes Database, named so because it was made for the development site saltine.net) is a small script written by Kyle Florence a few years ago that will store IRC quotes, it's like your own personal bash.org.
Bash on Rails is quote database engine (like http://bash.org/or http://bash.org.ru/) written with Ruby on Rails framework. Supports multiple moderators with different privileges, editing quotes, sorting quotes by rating, quote searching and RSS feed.
KuhAPI is the next generation application programming interface written in PHP 5.3 for quote systems like bash.org or something else. It provides easy access to the quotes while using new techniques and features of php object oriented design.
Perforins Bash is a "Quotes Management System" written in Perl. Users can submit chat quotes which will be checked by the administrator and then put into the database. It´s like the popular german-bash.org but open source!
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...Anna^ has a multitude of functions, including the ability to save small notes, quotes, haikus and more. She can also interact with various websites, like google and bash.org.
Kwotes is a chat quote database where users can submit quotes for review by others. Kwotes keeps track of the top rated quotes and removes low rated quotes. Kwotes is similar to the popular bash.org, except that it's publicly moderated and opensource.
IMPORTANT: As of 1 September 2011, I recommend that you download the fork of Rash here: https://github.com/paxed/rash-qdb-fork . Rash is a clone of the website bash.org. It was a project of mine in high school, and is no longer maintained.