Knots must be easy to untie and useable in many applications. The bowline is the most versatile and very easy to tie and untie. The figure 8 stop knot is easy to tie and untie and will not slip on poly line. These are my favorites but I also use 1/2 hitches cause they are fast and can be mullllltiplied.
BTW, a rope becomes a LINE as soon as it is attached to a boat Ropes are sold in hardware stores and Lines are sold in West Marine
I got a app. for that
this thread could also be called "What Knot to use"
when Im in a panic half hitches ,then when the adrenalin has worn off I go back and fix it.after consulting the app.
I studied a lot of knots in the Navy in my spare time at sea. The only ones I wind up using routinely while sailing are the sheet bend, trucker's hitch and the bowline. If you only learn one knot, the bowline is it--you can fake just about anything else using a bowline, and it'll never slip. They're about as secure as a shackle. A sheet-bend is a modified square knot that's made more secure by taking the bitter end and tucking it under the line rather than back through the loop--look at that animated knots site to see what I mean.
I keep looking for an opportunity to practice the rolling hitch, but as much as I like the knot, I haven't applied it in real life. As Mastreb stated, the bowline and a little imagination will pull you through. Some Knot Heads may say that the perfection loop and bowline are (k)not the same, but a perfection loop can be tied one handed and in a hurry; since my simple mind can't tell the difference, my vote is for the perfection.
IMHO,
you have got to be able to tie a bowline in the dark. no excuses.
a square knot, figure 8, half and full hitch, and properly tie a line to a cleat.
Ex Navy too, and out of all of em, bowline is clearly the most important. then I would vote "round turn and two half hitches". Those two are enough to do just about everything.
On a sailboat, you will want a stop knot too like a figure eight or stopper knot,, put this one in the end of your sheets to stop them getting away.
But just to look cool in front of other sailers, I'd add "Reef Knot" Sheet Bend" and "Clove Hitch"
They are all easy and nothing else is really needed . Master them and you will be set for life!
Last week was the maiden voyage of my x, and as said in the manual for the boat, I tried to tie a truckers hitch for the 2 to 1 advantage when tightening the main halyard. I however am not a trucker or a knot guru, so I ended up doing a rock climbing loop thing. Now that worked great and I really got my moneys worth out of that 2-1 ratio! Now When it came time to lower the main sail, I got the sail lowered a bit, but the wind was trying to fill the sail while I was trying to hold the main sheet and undo a stubborn knot. Now I couldnt just let the sail down because the knot in the line would have stopped at the top of the mast on the pulley and left the sail half way up(or down). This winter I'm definitely going to be learning proper knots and hopefully won't be in that situation again!
Agreed with others, bowline is number one. Number two for me is the ashley stopper knot because it won't pass through ANY rigging. Sheet bend and reef knot next. Having done about a decade more climbing than sailing I also use a figure eight and very frequently use an alpine butterfly to temporarily lock a halyard to a shackle when raising/dropping the sails.
For both climbing and sailing I learned a lot keeping a book of knots and a short length of line in the porcelain library in the off season.
I must agree with BScott, whichever knot you choose must be easy to untie. My first captain was an old salt retired from the Norwegian Navy. He didn't really teach us to tie knots as much as punish us for not being able to untie the ones we came up with. Swabbing a 92' square rigger alone was enough to motivate you to learn your knots well. Any knot you can't untie can easily cause a crisis.
He also taught us that if you want a permanent knot you should use a splice. The joy of being able to splice your own dock lines is underrated. A custom splice will barely fit over your cleat and never come off on it's own.
Twenty eight years ago there was a weekly show on learning to sail on PBS. I can not remember the name of the show, or find any reference to it now. Anyone remember it?
I remember he could throw a line around something and it would tie a bow tie knot all by itself. Seems to me he called it a bolin knot, but maybe I am wrong. Many years ago.
Ropes are sold in hardware stores and Lines are sold in West Marine 
,then when the adrenalin has worn off I go back and fix it.after consulting the app. 
