The only exception of that rule are insurances which cover stuff I might accidentally do to other people.
I buy insurance if either:
1. I believe I'm significantly more likely to break the item then their estimates (ex: you use your phone at your construction job, and are significantly more likely to break it).
2. It's enough money that it would cause significant problems for me (home insurance, renters insurance, etc).
Otherwise, I figure I am 'self-insuring', and will come out ahead over the long term.
Not necessarily. Insurance companies on average lose money from policies and make it up by investing the float. Think of the money they lose on policies as the "interest" that you get paid for lending them your premiums.
Insurance companies know the odds better than us, they set the premiums, and they still manage to make a profit every year (billions of dollars in lots of cases)
It glaringly obvious that "on average" the average person should not get insurance when not required, because otherwise you're just paying for the profit of said insurance company.
For example, I kill cell phones regularly from dropping them; for me, insurance might be more cost effective; for the people who keep cell phones turned off except for emergencies it probably isn't good value. But, anecdotally I would say that these are the very people who have insurance. They are buying 'peace of mind', a very expensive product created by Madison Avenue.