Homeowner's insurance isn't necessarily a small fraction of your income.  Some people are actually moving because they can't afford insurance (in the Florida Keys, for example).  Isn't that rearranging your life because of something that "might" happen?

I rent, but I still have insurance.  Even when I was so poor I had trouble affording groceries, I had renter's insurance.  A friend of mine lost everything in a housefire.  It wasn't her fault; her landlord accidently set fire to the place while he was trying to make repairs.  But she ended up not even able to go to work, because she didn't have any clothes.  That was when I decided insurance was worth it.  I've paid hundreds of dollars in renter's insurance, and never made a single claim, but, like the cliche goes, it's worth it for the peace of mind.

That might tie into "Why We Worry About The Things We Shouldn't... ...And Ignore The Things We Should" in a different way.

I'm sure the national average for homeowner's insurance is relatively low.

There are also folks who chose to take risks.  Around here it's people who choose to live in the canyons (fire, flood).

That doesn't disprove the general rule.

I'm sure the national average for homeowner's insurance is relatively low.

At least in Ohio, if you there is a mortgage on your home, the lender requires proof of homeowner's insurance.  

Around here (Ohio River Valley), the "risk takers" live in the flood plain.  They often are forced to take this risk bc/ the flood plain is the cheapest place to put a trailer and they can't afford to rent a lot elsewhere.  Theoretically, as flood waters come in, you could just pull your trailer to higher ground.  In reality, most of these trailers cannot safely travel and the occupants do not have access to a vehicle to pull them anyway, especially on short notice.  Many trailers were destroyed in recent floods (the worst being due to the remants of hurricanes Ivan and Frances that came all the way up to Ohio river valley roughly 10 days apart in 9/04).  Local officials have been trying to close down trailer parks in the flood plain or force them to build up the lots but it's hard to enforce as there aren't many alternative locations on flat ground around here that are affordable.

Now, I sometimes ask how is it that they cannot afford a lot outside the flood plain if these trailers all seem to have satellite dishes and the occupants seem to be able to afford a pack or two of cigarettes a day- but that's just my cynical side.

Problem I see with this is in the health-insurance area. Many people feel that one must have health insurance, even though costs are prohibitive for many workers. I gag at the thought of essentially paying 5 or 6 K$ per year to maintain a corrupt and inefficient industry, but this leaves me at risk. Rock <-> hard place.
FWIW, AVERAGE PREMIUMS FOR RENTERS AND HOMEOWNERS INSURANCE, BY STATE, 2003:

http://www.iii.org/media/facts/statsbyissue/homeowners/

Lovely! I see I live in the 1st ranked state
for highest renters and homeowners insurance.
(Texas). Looks like in most instances it is
double the majority of other states. To make
matters worse, we average $.16 kwh for electricity!
Leana, people who live in the Florida keys know that it's a matter of when not maybe!
Peace of mind?  You'd still have no clothes.  You'd still have all your stuff destroyed.  All you'd get was replacement money, which you could already have set aside in a high interest online bank account.  Insurance companies charge a lot of money to take all the risk out of life.  They make a lot of money at it too.  
Renter's insurance is a good deal.  There's a lot of insurance I don't have, but renter's insurance is a no-brainer.  Ditto homeowner's insurance, if you're a homeowner.  

I have online banking accounts, and none of them offer the kind of interest you would need to cover the cost of my possessions if the place burned down. Heck, even investing in stocks during the dot-com boom, it would be hard to turn my insurance payments into the coverage I have.