Your question depends really on what type of road obstruction you hit, whether it was moving or not, how much damage you caused your vehicle, and what your collision deductible is.
An example is hitting a large boulder in the road, damaging your car. If the boulder was just sitting in the road than the insurance company considers this an at-fault accident just as if you hit another vehicle. You will have to pay your collision deductible and your rate will probably go up due to your having an at-fault accident. If you have accident-forgiveness your rate won't go up for this one accident but you would need to be more careful for at least a few years.
If the boulder came down in front of you and was moving across the road this wouldn't be considered an at-fault accident. You would still pay a deductible but your rate wouldn't increase due to this accident. The same applies if, for example, you hit a deer that suddenly shot across the road right in front of you. That's a comprehensive claim rather than collision.
Obviously, if the estimate you get to repair your car is less than your collision deductible than it makes zero sense to turn a claim into your insurance carrier as there wouldn't be any coverage. If you hit a stationary object I think that the damage to your car would need to exceed your collision deductible by more than two and a half times before it would financially make sense to turn the claim in under most circumstances.
If you have young drivers in the household you should be very careful about turning any type of collision claim in even if the young person wasn't driving the car. Insurance companies get really anxious about any accidents in a household that has drivers under the age of 25 and can really increase the premiums in the event of an at-fault accident.