Let's say that a person has a $500 deductible on a home. Let's say that there would be a claim at x dollars. I think it's clear that if the claim was $501, that it wouldn't be worth it, due to higher rates, etc, but if it was $10K, it would be worth it. At what point do you think it would be worth it?
An article linked from cnn.com has some great advice, which I think are good rules of thumb.
Also, at least my insurance gives a premium price for those who haven't filed a claim in 5 or more years for homeowners or rental insurance. See if you have a similar discount, will loose it, and guess how much that will cost you over 5 years.
My rule of thumb: Your premium might go up quite a bit, possibly as much as triple, especially for a large claim. But, it is certainly worth it if you are going to get more than triple your premium through your claim. The worst case: Mortgage mandated insurance, which will be about triple your current cost.
At what point can you not afford the repair, and how will that repair affect your home?
In your scenario, you would be claiming $1, which I could agree is universally bad.
A good tip is to raise the deductible to the point you feel you can cover on your own so you aren't tempted. (It would lower your premium too)
This is what an emergency fund is for. In your examples, if you have $10K in an emergency fund, don't file a claim. If you have no emergency fund, and your roof is missing, I would suggest filing a claim.
If you have no money, but the claim is to fix something that you could ignore (missing a back porch? Lock the back door and don't go out of it) then save the $10K and pay for it out of pocket.
When it doubt, pay for it out of pocket if possible.
We learned the hard way on this one. First, our area was hit with what was called an "inland hurricane" where we forced to file a claim as our home received extensive damage.
Within the same year, we also incurred an electrical surge which took out our older big screen tv (one of those big monstrosities that sits on the floor). We were granted full replacement with a more modern flat screen TV, TV stand, and DVD player. It seemed like a no brainer.
We quickly found it as our premium went up that it wasn't that sweet. It wasn't a huge increase, but it definitely has us truly evaluate if it's really necessary filing a claim.