I think the first time I ever heard of the idea of "projection" was in the context of a burn.
"You're such a hypocrite!"
"Nuh-uh, you're just projecting your own hypocrisy onto me!"
Since that's excessively silly, I think it was some time before I took projection seriously as an idea.
Projection is a fallacy in which we attribute certain characteristics to others because we see them in ourselves. Most of the time, this is a very reasonable assumption to make, and one we make very often. If you ever want to understand other humans, the first and best place to look is in the one human whose experiences you have most access to: yourself. But we can take this too far, and when we do it's called projection.
I feel that it's almost too clinical to call projection a mere logical fallacy or cognitive bias. Projection is pretty much a way of life. No, the way of life. Everyone does it nearly every day. (I know this because I do it every day.)
This was illustrated in a recent Subnormality comic: We Assume of Others What We Know of Ourselves.
I recognize projection as a major source of my own irrationality. For example, I believe that if people only listened to my music, they would like it as much as I do. Never mind that even I don't like much of the music I liked in the past. I believe that because I don't get angry, neither does anyone else. Sometimes, my initial reaction to anger is laughter, since surely they are expressing anger ironically. I believe that since I don't like fashion or formalities, nobody else does either (they're just playing along). I believe that people are much less sexually active than they are. I have been enlightened by some statistics, but they still surprise me. The surveyor says many of his students expressed surprise at how common virginity was, but since I'm less interested in sex, my own biases are in the opposite direction.
What about you? What sort of things do you project onto others?