Under what circumstances will homeowners insurance generally pay for a new roof?

Yep, hail damage or after a severe wind storm where a lot of shingles are missing or damaged.

Hail damage is covered but you would need to report the claim at the time of the damage. You can't call the insurance two years after the fact and say, hey my roofer says I have hail damage. Also, they would want to inspect it to see if you actually needed an entire new roof or if it was repairable. If you needed a new roof anyway because it was just an old roof, and then a hail storm comes along and does some more damage, you may not get the entire thing covered. If you have damage, you need to report it at the time it happens or you'll play hell proving that the storm or whatever, caused it, months or years later.

Insuance covers a "sudden & accidental loss" caused by specific things (perils). Usually, hail is one of those, and most often the company would honor hail damages after first inspecting, provided you reported it timely. Windstorm is usually covered, as is Aircraft, riot, vandalism, eplosion, smoke & fire. However, just because your roof needs replaced, does not mean the insurance company will pay for it. It also wears out, and that is maintenance, not covered under the insurance contract.

Your homeowner's policy very likely covers this. You can always request a copy of that policy from the company. Any problems with the company can generally be worked out with the company, but remember that each state also has a department of insurance to help with such things.

Its important to understand the coverages on your policy. Keep in mind that your homeowners insurance policy is not a maintenance policy. It does not cover wear and tear. If you have 30 year shingles on your roof for 50 years and the roof starts leaking, don't expect that to be covered.