BuddyPress is an amazing plugin that has allowed me to create closed social networks without a lot of fuss. It includes lots of things that Facebook and Twitter offer such as "The Wall", "@" replies, and internal messaging. But it does some things that Facebook and Twitter do not do well such as groups with varying degrees of privacy and forums.
Because BuddyPress is built on WordPress, it is easy to take advantage of the many plugins that are available via 1-click install as well as enjoy all the fruits that WordPress, itself, brings to the table.
The BuddyPress plugin can be installed and activated in less than a minute.
I recommend this plugin for anyone who likes some of the features of Facebook/Ning/etc. but wants more control over the experience.