A social network service focuses on building online communities
of people who share interests and activities, or who are interested in
exploring the interests and activities of others. Most social network
services are web based and provide a variety of ways for users to interact, such as e-mail and instant messaging services.
Social networking has created powerful new ways to communicate and
share information. Social networking websites are being used regularly
by millions of people, and it now seems that social networking will be
an enduring part of everyday life. The main types of social networking
services are those which contain directories of some categories (such
as former classmates), means to connect with friends (usually with
self-description pages), and recommender systems linked to trust.
Popular methods now combine many of these, with MySpace and Facebook being the most widely used in North America. (from Wikipedia)

Facebook attracted 132.1 million unique visitors
in June 2008, compared to MySpace, which attracted 117.6 million visitors.
LSC Facebook page
Des Moines Area CC Facebook page
College Admissions Facebook app
UMD bans Facebook for athletes
Citizen Media Law Project on UMD ban
Facebook ads: Blog post w/comments
Facebook ads: a negative experience
Facebook Ads vs. Google AdWords (one view)
Another social network service that has been making a big splash lately is Ning. 
A Ning network is free (ad-supported) and can be customized by the site administrators to include many different communication tools and include all kinds of web-based content. They can be totally public, totally private, or a combination of sorts.
Classroom 2.0 (mainly K-12) has 11,664 members (Sept. 2008)
e-Learning 2.0 Ning site
Minnesota Mooseworks - mainly MnSCU people (private network)
Naturally forming Ning networks seem to be fairly successful, but "forced" network creation hasn't proven very successful. If you build it, they might not come.