I'm actually not positive what I'd save. I have all of my important files backed up in a remote location so I wouldn't be at rick of losing anything. Insurance would pay for a new computer anyway.
I'd save something irreplaceable if I had the time. Something like old photo albums or old drawings. Both which can be scanned into a computer and saved I guess, but it's nice having originals of things like that.
Cons, you should pay about $20-$30 a year and get a safety deposit box at a bank. It'll make you feel a lot safer should you ever lose your external HDD somehow. Just keep a spare in the safety deposit box with all of your important works on it.