Rbruce, I would add a fishermans knot, or bloodknot, to that (I think they are the same knot).
Hikermor, the square not is great, when the lines are under tension. I have used it many, many times, backing it up with a half hitch, for climbing, and general knot tying around campsites. Its easy, and secure, when used for the applications the know is intended for.
IMHO, there is no real reason to learn more than 9 knots-other than for fun. If what you are trying to do cannot be done with the knots that rbruce has listed, then you are either in a REAL bad situation, or you're a sailor .

On that topic, I recall reading about the old whaling days, and all the pirate and pole exploration books that boys read when young (or used to), and I was always fascinated that sailors knew how to tie these intricate knots, and knew for what applications. I used to think it would be cool to be a sailor, just to learn the knots! Ah, the simplicity of youthful dreams!