I was a student at Caltech on and off from 1983 to 1990. During part of that time, Feynman taught a sporadic class intended for freshman (although many others attended) which was called "Physics X". There was no credit for this course, and no registration required. In fact, it met at 5:00 PM on a Friday (maybe he only wanted to see the more dedicated students?). The amazing thing about this class was that there was no curriculum. He would show up to class, pick up a piece of chalk and ask if there were any questions. Whatever topics were raised were the subjects of discussion. The questions did not have to be strictly physics related - he would derive equations for the operation of a flute and then later relate how he managed to open the safe at Los Alamos one night in order to prove that the security wasn't good enough for protecting their notes. When asked how he was able to remember all of the equations (he never had any notes for this class), I heard him reply that he didn't need to remember all of the equations. As long as he could remember the first principles he could always derive what was needed.
I sometimes attended graduate physics seminars as a freshman to see if I might hopefully be able to absorb anything. Usually they were mostly over my head. I remember attending one seminar at which Feynman was also in attendance, sitting toward the front of a large lecture hall surrounded by a few colleagues. The lights were dimmed, and the seminar was presented by a graduate student from a prestigious East-coast university that shall go unnamed. As I recall, this was a presentation of his doctoral thesis work which he in the process of completing. I didn't pay too much attention to all of the overheads, as the math was beyond me, and I noticed that Feynman's head was bobbing and he seemed to be dozing. After about half an hour of rather tedious equations with no audience participation, Feynman's head suddenly jerked up and he said loudly, "You can't do that!" The confused grad student froze in confusion, then asked what it was that was wrong. Feynman made a brief reply, and then some of his colleagues, apparently in the belief that he hadn't been paying attention and was confused, tried to defend the student. Feynman then jumped up in disgust and went to the board to scribble up a few equations. There was a somewhat stunned silence. From what I was able to gather, the student had somehow mixed equations related to wave and particle theories of light in a way that they couldn't be used together. I don't know if he was able to salvage any of this thesis work - but it pretty much put an end to the presentation. I felt a little sorry for the grad student!
I bought a set of the Feynman lectures and had them hardbound (only softcover were currently being published), hoping that I would be able to get them autographed. I waited too long however, not knowing of his illness, and he passed away before I had a chance to ask him. I had been a little bit nervous about it, having heard the story of a High School physics teacher who approached him in the Athanaeum parking lot with a request for autographs. Apparently he had been about to sign, when the gushing teacher made a remark that he thought the lectures should be required reading for all students. This upset Feynman, who refused to sign saying that people should read his books because they want to read them, not because they have to.
Feynman was well known and admired among the underclass students, with whom he loved to spend time. There was a memorial service held after his death, at which I worked as an usher. I was fortunate at this time to be able to briefly meet and assist Stephen Hawking, who came to the service. I find that even briefly experiencing the "presence" of individuals such as these gives me the will to live a better, more worthwhile life. My own father, an outstanding research chemist, passed away a few years ago. To relate the bad news he had received from the doctors to my mother, he said, "Well, I've been given an incredible opportunity!" He meant the opportunity to discover what lies beyond the boundaries of death. Feynman's final comment makes it sound like he wasn't interested in the subject. Maybe he considered it something like a black hole, where what occurs on the other side of the event horizon has no importance, since it can't affect events on this side. But I have to think he was pretty interested - and probably just didn't want to show it.