Yes, your auto insurance rates could go up if you have an accident and it is entered in the insurance records.  Some insurance companies forgive the first accident and some others may charge a little extra at the time of your signing up for offering forgiveness. The specific details of this clause vary from state to state as each state has its own laws and regulations.  Some other companies will not increase your insurance rates if the cost of damage due to the accident is less than a specific dollar amount. Whether the insurance rate will increase or not if you had an accident depends on various factors.  

If you are concerned about the premium rate increase due to an accident, you can speak to an insurance expert to get help in canceling or minimizing the increase.  You can also approach consumer protection groups to get free advice and guidance.  Whether you were responsible for the accident is the main factor that determines if your auto insurance rate will go up or not.  If you were at fault, your insurance company is likely to add a surcharge on your premium.  The amount of surcharge is related to the extent of damage and the insurance company. This may be around 10 percent and will stay for three years.  You are at fault to what extent is also a factor to be considered. If you are at fault by a less percentage your surcharge will be less than the one with the higher percentage of fault.  

On the other hand an insurance company can increase your rates even if you were not at fault.  The average rate increase will be around 20 to 40 percent every six months. This is possible when the insurance company examines your insurance record and looks at factors like past claims, their frequency, the severity of damages and how long you have been with them.  This rate increase is due to the fact that you have become a higher risk to the insurer.

If you had availed a discount on the basis of good driving record, the discount will be withdrawn as a result of your accident.  This means your insurance rates will go up even if you are not charged a surcharge.

You may also get free accident forgiveness for a slightly higher price from some insurance companies. This is like a prepayment of a surcharge but there may be some other limitations so you should go through your policy carefully and understand these clauses.