A work colleague of mine and otherwise very good friend does indeed believe that the moon landings were fake. It took some time until she started admitting that during our chats, and I have to say that I was at first baffled that she actually believed that they were fake and I've only recently stopped mocking her about that.
I also met a friend of a friend (man, late 30s, otherwise quite a great guy) who told me straight-faced that he believed that the Holocaust was not real, that the numbers were "exaggerated" or somth like that. I couldn't continue the conversation because I felt that there was nothing much that I could say, you cannot really continue that kind of conversation without calling said person an anti-Semite and it all goes downhill from there.