Free software(PHP):
Jcow - http://www.jcow.net
Basic social networking features, plus optional applications(extensions).
Elgg - http://www.elgg.com
popular social script. It is focused on the feature of “Groups”.
Phpizabi - http://www.phpizabi.net/
Focused on dating feature. But seems long time no updates.
Joomla community builder - http://www.joomlapolis.com/
Based on Joomla CMS. They provide free&paied editions. The free edition is limited on the features,.
Drupal community modules - http://drupal.org/node/206724
a list of drupal modules which will help you build communities based on Drupal.
Remotely-Hosted software:
Ning - http://www.ning.com
You can generate a social network online. It is free, but there will be a monthly fee if you want to increase the bandwith or remove their ads from your network.
Socialgo - http://www.socialgo.com
Similar to ning.com.
Kickapps - http://www.kickapps.com
In version 3.0, it was implemented more social networking features.
Google Groups - http://groups.google.com
It’s like “forums + newsletters”.