Stephanie Buckhanon Crowder makes one of those points that ought to be obvious, but isn't, namely that it's totes OK to not share everything and the kitchen sink with one's students. At the same time, as someone pointed out in comments, it's pretty much a given that students will be curious and poke around a bit on the internets. Which means that there is sharing and sharing.
My own rules, developed by ye olde method of trial and error:
1) In general: discuss "students" in only the most general of terms; try to avoid anything that could be pinned to one student, or even a specific group of students, unless it's wholeheartedly positive. I know that some people get huffy about this, but I'm not anonymous, and my students haven't asked or given permission to be identified. If you're anonymous, then obviously you have more freedom in this respect, but even so, bear in mind that one day in the distant future, your anonymity may be breached (either because somebody snoops or, even more likely, you accidentally identify yourself, whether on- or off-line).
I also tend to be somewhat chary about discussing my personal life, because it's, well, personal, and not something I tend to do in the "real" world, either. Photos of cats are OK, though. Oh, and book acquisitions.
2) Facebook. Completely locked down. No requests accepted from current students, because a) if I am going to post something personal, it will be there and b) surely my students don't want me seeing their personal life. However, I decided some time back that rule #1 would also have to apply, simply because you never know who is going to cut and paste you.
3) Twitter. I've followed and been followed by students on occasion, but neither seek them out nor dissuade them. (I've done Twitter-y things in courses before, but many of our students don't use the app, and I'm not going to make them sign up for it.)
4) Here. Obviously, students can find me here (and have, on occasion).