I remember a few - for example someone would introduce themselves as a lawyer and then point out that some clauses in t&c are illegal and that he will report it "to authorities" (and sometimes they would offer "help" if I pay), or someone would upload their nude pictures and then report this to hosting provider that the website is showing these pictures without their consent. Some people would demand that I give them access to private messages of their "partners" and would threaten me that they will find me and "sort me out". Sometimes I had technical issues where the server would go down for a couple of hours - so there was a profile of a local band, something like a Facebook pages are now, and they made a post about the concert they are going to have, but the server was down on that day and they blamed me they lost money because just a few people came to the concert. I also had someone claiming to be a partner of one of the users demanding that I delete his partner account as she ignores him and only spends time on the website and sent me my home address. Very stressful.

edit: I remember one more. One guy would post his nude pictures typically exposing his face and his bottom and then he would write his name and address and add messages like "beat this guy up", "come find me" he would register other accounts and then post degrading comments under these pictures of himself. I initially thought that this is some kind of revenge and I was promptly deleting this and removing these accounts. Eventually that person would write that this is turning them on and was very upset that it gets deleted. It's when I added IP blocking and blocked all addresses he used.