Sorry to top an old post, but i just found my way to these forums and knots are 1 of the things i love to play with.
I'd like to break down the reasons along with my picks, so here goes:
1.square or reef knot- its simple and it can be rolled over for easy removal, hence its use in first aid. But also very desirable in other circumstances.
2.bowline & sheetbend- if you look at these 2 knots they are actually the same. by learning 1 you learn both which extends its usefulness and cuts down the learning curve. So, you have a knot which can join 2 lines or create a solid loop.
3. clovehitch & 2half hitches. Same principle as above. when you tie 2(or preferably 3) half hitches you are actually tieing sequential clove hitches around the line. This adds multiple uses to one knot.
4.Alpine Butterfly knot. The other 3 knots provide for joining lines, creating loops, lashing, and tensioning. This 1 allows you to create a non slipping loop in the middle of a line.. It can be used for a compound tensioning system, tieing a safety loop, several in a row can form a rope ladder. And its very easy to learn. But most books i've seen dont show the easy technique. So, bear with me and I'll give it a shot....
First its important to note that you dont need access to either end of the rope. Turn your palm up. Lay the line across your palm, wrap it once around your hand. Now wrap it again around your hand but lay the line between the first two. Take the wrap closest your fingers and pull it across your palm and over the other 2, then tuck it back under them. keeping hold of the piece you tucked under(this will be your loop), slide it all of your hand and work it tight. You should have a loop coming out of your line perpendicularly.
Hope this helps.
Dave