"Professors do talk, you know" - What exactly does that mean?
Since students are a big part of our life, we discuss students both in casual situations (e.g., lunch) or professional settings (e.g., committee meetings).  Of course you shouldn't think students are all we talk about, and discussions about students mostly only come up in committee meetings when they're relevant.  
The conversations are mostly professional, particularly the ones in meetings, but some things you might consider "gossipy" I would consider professional, e.g., where a student is going for grad school.  (As a department, we have an interest in what our students do afterwards).  Not that there is not no gossip going on, but at least I personally am not so interested in it, and I don't know too much about the personal lives of most of my students.  Most "gossip" is about other faculty.
Well, faculty often discuss about bad experiences with/performances of students with other faculty. Sometimes to get advice, sometimes to vent, and sometimes because the student has done something amusing.  Sometimes the student's name is used and sometimes it is not.  In my department, I think the student's name is not normally used in the case of undergrads unless it is in a professional context (needing advice or reporting a possible problem student).  But we don't often give explicit advice like "stay away from this student."
In general, I think people have a tendency to spend more time complaining than offering praise.  However, at least at the undergrad level, when names are used, I think it is more often to speak positively or neutrally of students than speak negatively.