DISCLAIMER: YMMV, check with your insurance company for details on your own policy and/or coverages.
Generally speaking, there is a threshold limit on accidents in each state. If there is an at-fault accident, and the total damage is over that limit (not per car, but per accident) then typically the at-fault person's insurance goes up. You'll need to see if there is any sort of accident forgiveness program in your state. Usually, you need to have a clean driving record for about 5-7 years since the last at-fault. The time period could be either for the household or per driver. If there is going to be an increase, it will happen at the next renewal of the insurance after the date of the accident and will last for 3 years.
Daywane:
Since your vehicle is now considered a salvage vehicle, you can now remove any comprehensive and collision coverages. Your insurance company has given you the value of the car. If you do decide to keep comp and coll on the vehicle, you will still have to pay the full premium while only getting any payout/repairs based on a salvage value. Personally, I would keep the comp to take care of glass/Mother Nature/animal damage. Depending on the age of the vehicle, it might not make a big difference between a large deductible and a small one.
pinballjim:
If you live in FL, you already know several companies are moving out of FL or limiting their business for homeowner policies. Some insurers will insure the house, but exclude windstorm damage. The DOI (Dept of Ins) doesn't want companies to charge what is right in order to keep insurance rates down and to keep voters happy. Citizens (state run insurance comp) is insuring about half the state last I remember, and they're supposed to be the insurer of last resort. If a big hurricane runs through FL, the state is going to be on the hook. Most homeowner policies specifically exclude flood (covered by a government policy, FEMA, I think) and earthquake (which can be "bought back" in most states). A lot of policies may have a seperate deductible for windstorm.