All seacocks should be kept closed EXCEPT ..
There is one exception to Peggie's dictum: scupper hoses should be left open.  If you close those seacocks, rainwater will fill the cockpit, and if it gets high enough, enter the boat through the instrument panel, etc.  Scupper hoses are a short unbroken span, heavy-duty, and double clamped, so they are a good deal safer than the engine cooling system.  Fortunately, newer boats are designed without scupper hoses.RULE 1: All seacocks should be closed when not in use.  (You think it is safe when you're on the boat?  If you are sleeping, will you wake before the water reaches you?  Alas, scuppers are always in use.)RULE 2: Whenever you put a boat in the water, have someone on board, to check every through-hull and the bilge for unexpected water flow.  Do this before the travel-lift straps are removed!