It is possible to use some social networking platforms in the classroom.  For example, Dale Basler uses Twitter with his HS physics students.  You should also check out this example of how to use Twitter to bring current events into your classroom. However, there are a few platforms designed specifically for classroom use -- and student privacy.

Social Networking can increase the communication between students in your class. However, it likely will not happen spontaneously.  You may need to have specific expectations (and assignments) to help students effectively use these networks for school purposes.  Research on the use of blogs and online discussion platforms as an addition to face-to-face courses has shown a positive impact on in-person discussions.  Many students prefer the pace (being able to carefully think through their thoughts) and feel safer in online discussions.  This builds confidence that leads to increased face-to-face classroom instructions.

Here are two online social networking platforms for you to play with.

Edmodo

Edumodo has been around for quite a while and has a lot of robust features.  This is probably your best bet for introducing social networking and "virtual" discussions into your classroom.

Collaborize

Collaborize is an easy way to create discussion forums for your classes.

Ning

Ning gives you a full functioning social media platform with blogs, discussion forums, video upload / file sharing, and messaging.  You have a lot of control over access and privacy.  There is a small fee to create a classroom Ning.

Twiducate

As the name implies, Twiducate functions very similar to Twitter.  However, you can easily create and manage your students' accounts.  You can use hashtags (and search for tags) just like on Twitter.  It appears that you can use more than 140 characters too...