I learned my knot lore in the Boy Scouts. Of all my BSA skills they are the ones I've used the most. Here at work, engineering firm, I have boiled it down to two basic knots I teach the guys here. The square knot and the bowline. A person needs to know at LEAST those two knots. All the people here can do those two. I can still do a sheepshank, a sheetbend, a clove hitch and a tautline hitch also. Everything else, to me, is just gravy. Everything is smoother in a campsite if you've got at least one guy that can tye the knots listed above.
Uses of the above knots:
Square--joining rope of same diameter
Bowline--making loops, very important for rescue operations
Sheep Shank--shortening rope
Sheet Bend--connecting rope of different diameter
Clove Hitch--lashing, you'll never get a good lash without this one
Taut Line Hitch--ajustable tightening as for tent ropes
These are the basics. Try to know them all, and if you just can't get them, learn the square and bowline at least.