Perhaps this could be a place for us to collect info on such things.
So to begin...
We begin with the Bowline. THE classic fixed loop in the end of a line. There are many good ways to tie this knot and get the same result. The method that follows is my personal favorite. This method can also be adapted to a one-handed bowline, here's a demonstration: Video
We start with a bight in the line. The end is brought over the standing part, and with an overhand twist we then pull the end up. If done correctly, this forces a loop to form around the end. From this point on the method does not differ from those above.





A relative of the Bowline is the Sheet bend. This knot was used by sailors, or really anyone who needs to attach a rope to a sheet, sail, tarp whose grommet have torn out, etc. It is also well suited for connecting two lines of differing size. In these pictures the black rope represents either the thicker of the two lines or the sheet. Note the orientation of the ends, this is important (and in these pictures incorrect--I just haven't taken new pics yet). The ends should emerge on the same side of the finished knot. If stability of the knot is a concern, try the Double Sheet Bend. Simply continue around the knot, and tuck a second time.



