First of all, to be a little bit pedantic for a moment, on a boat "Bungee Cord" is more properly called ''shock cord''. Growing up in sailing it was considered rather luberly to call it ''bungee chord''. Another similar pet peeve is calling ''Fenders'' ''Bumpers''. I know I see this all the time including in catelogs but technically they are Fenders because they are they are there to fend off and not absorb collision.
Back to the topic, there are a lot of uses for shockchord on a boat. I have several sets of shockcord with a hook on one end permanently attached to my toerail at the bow that I can quickly pass across the deck to belay my jib in a hurry when I drop it. I have loops of shock chord on my docklines so that they do not abraid my topsides. I use these same loops to hold my docklines across the inboard end of my slip so I can pick up my stern lines without getting off the boat when I am single-handing. I use shock cord to secure the bottom of the fabric wind scoop that I set on my forward hatch. I don''t use it to secure sails as I think that the tension is too harsh on the fabric prefering to use traditional webbing sail ties in stead. I use shock chord to hold my tiller while I am singlehanding and need to leave the helm or to hold the tiller on center when I am not underway. I use shock chord to gielguy my halyards away from my mast. I use shock chord to hold open lockers and hold lockers shut. The list is nearly endless.