I think that blogging could be very cool as a teacher, especially if used in a smart way. Once you are committed to having a blog, my first step would be following as many teachers as I know along with education blogs that I could get useful information out of. Once I have people that I know following me, I think that a great way to use it is to post my low points and high points in teaching. This way, my readers could feel like they are not alone in these low points and get great ideas with my high points. Along with this, for my low points I would hope to get comments on advice on how to help my issue from helpful colleagues.
When talking about how my students can use blogs, I could go about it the same way. Depending on the ages, I may have them make a blog, and every once in a while (maybe every friday, or maybe once a month) have them do a sort of classroom evaluation on what they like or dislike about the class. This way I can get feedback on my ideas and classroom management and try to tend to students who are not liking my teaching style. A different prompt could be highs and lows or that week/month, this way I can form a relaxed sort of environment to gain a relationship with the student. One last idea is in a way using both of these, but instead change the prompt every week/month depending on what you are looking for from them.