Twitter, Facebook, Google Plus, the many systems made for education (Twiducate, Edmodo, etc). Which do you use? Many schools and teachers like to use systems like Edmodo and Twiducate because they can keep things private and see who is accessing the information. Many schools use Google+ and set up Circles to keep things private and organized. Others just use Twitter and Facebook. It all depends on your needs, policies, and what you are trying to do with the system.
Here are some articles on different social networks and what they are useful for, as well as some course management systems that include social networking features. Below them, there is a great infographic from business consultant network Zintro on social networks and when they are best used for what purpose.
Related:
Twitter, Facebook, RSS feeds, Email, Google+ - why/when use each one
Twiducate - free social networking for schools
Social Media in Education - connect, share, learn, communicate and more
EDU 2.0 Free Course Management System for Schools
5 Great course management resources for educators
it's learning Course Management System
OpenClass - Pearson and Google combine to make free LMS
Learnboost online planner/gradebook announces new admin features
5 Great course management resources for educators
it's learning Course Management System
OpenClass - Pearson and Google combine to make free LMS
Learnboost online planner/gradebook announces new admin features