I have a list similar to Jamie's. The only other one I'd add would be a carrigh bend, as that doesn't slip under load, where a sheet bend might. Ashley:s is a great book on knots, but I can also recommend "The Marlinespike Sailor."
You needn't know hundreds of knots. Knowing a good stopper knot (like the figure eight), bowline that's just so darn handy to tie things together, tie to one thing like a loop or fence ot tent pole, a bend to join two pieces of rope together, a truckers hitch for having a loop on the middle of a piece of rope that can help secure things, a clove hitch to keep things tied up, and a car right bend for when you're marrying ropes from two different things together ( such as towing something) takes you pretty far.
I learned them by using a pair of old shoelaces and a pencil or pen to stand in for a fence post or dock. It was easy enough to practice pretty much anywhere, and helped me to learn how to untie the knits, too.
Another knot I've used idms a monkey fist. Helpful if you have to throw a line pretty far and you want to add some weight to the throwing end. Came in handy for me when I was throwing a bit of rope up in the air, hoping it would wrap around a high branch. My cat was stuck in a tree, and I though if I could hoist up a basket he liked to nap in, he might be willing to climb in. He wasn't, but eventually made his way down all the same.
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