Storing Your Rope
(2 Methods)
The first of two methods I'll describe is shown above.  It goes by many different names including an Electrician's Braid and a Doubled Monkey Chain.  Parachutists use such a method to keep their chute cords from tangling.

Double up the rope by grasping the two ends together and make a slip noose as shown in step "A".  Then, reach through the loop just made and pull a
bight of doubled-up rope through it to make a new loop.  Continue reaching and pulling loops until you get to step "C".

If you reverse the last move correctly, the whole thing should cleanly unzip with a single tug.  This can be tricky sometimes.

Most find it easier to finish the chain by almost pulling the last double loop all the way through, but then taking single bight leftover (the middle of the rope), and and throwing this single bight over the final double bight, as shown in the
"Improved Method..." diagram.  So when you want to undo it, you just pull on the only single bight available.

This method is especially effective in keeping your rope tangle-free when you need to wash a filthy rope in the washing machine (air-dry only to prevent heat damage).  Switching hands halfway through the braid helps reduce kinking at the end.
For those of you who prefer standard coils, try the Figure of 8 Coil, shown above.  Again, start by grasping both ends together and coil up the doubled-up rope around your arm until you get to the bighted middle of the rope.  Then, take this leftover bight and wrap it around the coil to make an eye and push the bight through the resulting eye of the coil as shown.  If you prefer, you can start coiling at the middle of the rope.

You can use the loop to hang the coil.

Related page:  Buntline or Gasket Coil, Fattened Sheepshank

Figure of Eight Coil
Improved method of finishing the braid
Electrician's Braid