We have filed a few claims over the past 10 years, including:

Water damage due to a sudden burst of a pipe. Required expensive drying of walls, replacement of part of the drywall and replacement of the flooring. Dealing with insurance was extremely pleasant.

Burglary of house. Lost laptops, camera, time machine, diamond earrings. Similar experience. Surpringly, the rule was: if you want to be reimbursed in cash, you get the current value (which is close to zero for a 6 year laptop). But if you buy a new laptop, you get the original purchase price reimbursed. “Hello new MacBookPro!” Zero complaints about the insurance.

> time machine

Wow! How much was the replacement cost for that?

probably talking about https://en.wikipedia.org/wiki/AirPort_Time_Capsule, which works with time machine (the software)

Yes, that. :-)

Insurance paid for all of a new roof after my 14 year old roofing was struck by a hail storm. I’ve heard of others having problems with various aspects of insurance, though, and given the size of the insurance market, statistical patterns or data would be more useful to read than posts by one or two people on HN.

I tried finding data on insurance payout/refusal rate when I was considering switching to a cheaper but lesser known car insurance company. It doesn't seem to exist. So much for consumer choice.

Which company? I know State Farm isn’t good

Farmers.

Insurance companies, to my knowledge, almost always pay out for "normal" claims on standard policies, with some reasonable exceptions. That's why when they don't, it's news. You may not get all that you think you deserve, or you may get more (after the 2011 tornadoes, our insurance paid for a new roof, although only about a third was damaged by the falling tree).