Yes, this is a problem. I think the biggest thing I fear is poor health. I live in Japan which has a health care system, but it can still be quite expensive to be ill. Also, my wife and I won't have children probably, so while that saves money up front, I have nobody to look after me when I get old.
Insurance is my main hedge against these risks. I try to follow a healthy lifestyle as well. I used to keep fish and it's amazing how much longer fish live when they aren't stressed. I try to replicate that. Finally I try to buy long term, low risk investments (like government bonds) with my excess cash. However, I keep a few years worth of money available in liquid assets for things like disability.
Probably the biggest risk is getting a mental illness that isn't covered by long term disability insurance. I have no idea how to deal with that one :-( All of my skills to live simply may be useless if I lose the mental ability to use them.