We used the following 6 basic knots teaching students in the ASA:
Bowline, Fgure Eight, Cleat Hitch, Reef / Square Knot, Clove Hitch, Round Turn and Two Half Hitches. Then we'll added the Sheet Bend, Rolling Hitch, and finally the Trucker's Hitch for the next two classes. I use the Bowline, Reef, and Trucker's knots almost daily away from the boat. I'd say these 9 would get you through most any sailing situation. If I were to name 2 knots to know in your sleep, it would be the Cleat Hitch and Bowline. The Cleat Hitch will be what you need to do to secure the boat when you're tired and cold and the Bowline will be the knot to save your life in an emergency such as someone falling overboard or needing a tow away from terra firma.