Basic engine repair skills, something to patch up your boat in case you spring a leak, a basic comms kit+genny so you can call up the coast guard or a passing boat if you should need them (assuming your island is out of cell phone reach), cache of freshwater, fuel, waterproofed matches and a couple of days worth of tin cans in case you ever get cut off. Halifax coast in winter can be, how to phrase this, impressive, to say the least.
Mind you, the real kick is when you are isolated but there is an additional degree of risk there. No need to get your appendix out as a precaution just yet ;)
All of this is assuming you're on the salty side of things, if you're in a lake it's a lot more relaxed but you will still need to take basic precautions and you'll need to be extremely careful with what you do with your wastes (you'd need to be just as careful in the ocean with that for ethical reasons but there will be fewer watching eyes so you can drop the 'extremely').