Some of the more disturbing threats I've received in my academic life were:
1 - undergraduate: A practical joke that a friend played on me (because I had played one on her and well deserved some sort of retaliation) backfired. The joke was to advertise widely that I was associated with a particular repugnant political group. I got death threats until the college president intervened with a college-wide announcement. There were even announcements to this effect on the local radio stations, as the death threats had included mention of snipers targeting me on and beyond campus. My friend felt worse than I did about this all, and yes, we are still friends.
2 - graduate student: A male student in a lab for which I was the teaching assistant kept asking me disturbing questions, ranging from "Do you walk home alone at night?" to "Do you worry about being raped?" and then even "Would you like to be raped?". I reported that one, but no faculty in my department thought it was serious enough to discuss with the student, and I was too clueless to talk to anyone outside my department about it. Friends walked me home for the rest of the semester until we all felt that the threat was gone.
3 - professor: An unstable postdoc told the department chair that several faculty (including me) and a grad student were trying to kill her. The postdoc then had a personal chat with God, who gave the postdoc permission to do whatever was necessary to make these faculty and their families suffer. There were some scary incidents involving broken glass, knives, astrology, theft, and the postdoc's showing up late at night in the department (and in my office) even once denied after-hours access to the building. The department chair refused to call the police, but he did fire the postdoc, which then involved a loss of visa status.
There have been others, but those are some of the more memorable. So far nothing really bad has happened to me or my colleagues, just some anxiety and stress. In another case, however, an unhappy grad student threatened some faculty (including me), got some professional help, seemed to recover, and then committed suicide a few years later. This was really tragic and shook everyone up, but one of my colleagues commented that he was just glad that the student didn't decide to take some others along when the suicidal urges became so extreme.
11 months ago