Examples. I have to give more examples. The baffled looks of my students in one of my classes seemed to fade away as I went over specific cases instead of general rules. It's hard to think like an undergraduate at times ... they like specific numbers, though, and I should remember that.
One of my students is actually a grad student, and he invited me to see his talk, the first hour of a graduate seminar course. He apologized repeatedly in case it might prove too basic for me (I'm rarely bored by material ``too basic,'' even in the odd case when it is); and, I went. It turned out he'd invited three of his instructors to witness his talk, and didn't mention it to the other students or that class's instructor, so we had some slightly awkward greetings. Still, it can't hurt to be on smiling terms with more people.
Unfortunately in the attempt to explain everything his audience needed to understand his topic, he ended up asking everyone -- one by one! -- if they were following, and he plunged into an attempt to describe a full course in real analysis, going into further detail to the point that any traces of the original problem were completely lost. A good proof is a narrative; you can't explain it by explaining every detail, but rather by describing the plot and filling in the surprising. The seminar instructor made essentially that same point to explain where things went wrong. I don't know if I'm invited to future seminars.
Trivia: Lunar Orbiter I's pictures of the Earth from the vicinity of the Moon were not in the original flight plan, and Boeing had to be convinced to add the pictures to the program. Source: Destination Moon: A History of the Lunar Orbiter Program, Bruce K Byers, NASA TM X-3487.
Currently Reading: The Paper: The Life and Death of the New York Herald Tribune, Richard Kluger.