This is one of those topics that has the potential to fill a silent room with a heated discussion. No, I'm not trying to start such a discussion; I just want to share some clarifications about the Facebook environment.
Facebook provides various tools for social networking. There are personal profiles and there are pages and groups. I think that there is a tendency to overlook this fact and use the wrong tool sometimes, and that can lead to eyebrows and questions being raised or to bigger problems.
If we try to equate the Facebook environment to the offline-world environment, it may help us better understand the options and implications. The comparison would be something like this. Your personal profile is like your home, a Facebook page is like the information desk in the lobby of a building of an organization, and a group is somewhat like a conference room or a meeting place.
For friends and family, we share our profiles by becoming friends, in other words invite them into our homes. They can see all the pictures on the walls, get a closer look at out hobbies, living style and other personal information that we openly display throughout our homes.
Pages are for public figures, and Facebook treats corporate entities as these figures as well. So, for example, Tim Burton might create a personal profile for his friends and family, and a Facebook page for all his fans. Similarly, IU Schools and departments would also create pages to disseminate information to faculty, staff, and students. Anyone who "Likes" a page, sees updates from that page, on their wall.
Facebook groups are then the perfect place for faculty and students to "meet." The group model matches up perfectly with the class model. A group provides the students a place to discuss ideas/topics with other students or ask the instructor questions, and a place where the instructor can post ideas, questions and answers. As members of this group, the instructor as well as the students see group activity on their personal wall, but their personal information is not exposed. Groups also provide more control over permissions and memberships, so you could say that these are meant for ... uhm! ... groups of people.
So, if you really are friends with your students, you may feel completely comfortable inviting them into your Facebook-home, however, you should also take a look at the Facebook FAQ for some more detailed information about these and other tools to help you make a better decision about the best way to integrate social networking into your coursework.