The single-strand Double knot is just an extension of the Simple knot. Being considerable bigger than the Simple knot though, it is an ideal terminator for a Slip knot. That is, the Double knot will not allow the end of the line to pull through the turns of the Slip knot, once pulled up tight against the turns.
Another possible use is to prevent a Prusik knot from pulling through, since they do tend to work through a bit after being locked and unlocked numerous times. So far, I haven't had any trouble just using a Simple knot as the terminator - but you could use the Double just for peace of mind!Now, if you really want to go overboard with knot-tying...
If you ever need to cut and then re-join a piece of bridle line, the Multi Strand Double Knot is handy. It's so easy to do, and that extra turn of line makes it slip-proof. Unlike the Simple knot when connecting 2 lines!
I also use this knot for flying line, although it probably reduces the breaking strain significantly. But no more than all the accidental knots and frays that a well-used line tends to accumulate anyway! This is not so much of a concern in a bridle since in that case the strain is shared between 2 or more lines.
Apart from modifying a bridle, this also comes in handy when scrapping old sail and re-using the horizontal spar(s).
I actually did this during the trials and tribulations with the
very first build of the Dowel Roller kite! The old bridle lines were
snipped so they could be fed through holes in the new sail.