Sweetter 2.0 – an “open source and fun microbloging service . . . being develop[ed] by SUGUS (group of GNU users from the University of Seville).” Go here for code. Based on TurboGears, a python-based web application framework. Affero GPL (AGPL)
Jisko – Affero GPL (AGPL) licensed framework for microblogging, PHP 5 and MySQL. I had to use Google Translation to try to read the wiki, as I no hablo espanol.
Yonkly – written in ASP.NET by Emad Ibrahim. Code hasn’t yet been fully released but you can get an early version here. (License is not yet specified though it is described as “open source.”)
Twoorl – a GPL (3) implementation of a microblogging service in Erlang using ErlyWeb. Started (and entirely written?) by Yariv Sadan
Prologue – not really a microblogging platform per se, but a WordPress Theme which could be used as a microblogging platform. (Note that the Prologue post itself kills Firefox 3 for me – caveat browser). Prologue is available under the GPL, as is WordPress itself.
Laconica, which is the software which powers Identi.ca. Also Affero GPL (AGPL). This is perhaps the most robust, and is based on the Open Micro Blogging protocol. It also embeds creative commons licensing on the content people publish, which I think is great but others may have issues with.