Now this one can be a bit tricky.
If you are at fault for an accident, like if you rear end someone then there is a very good chance your rates will go up.
Now, there are a couple of exceptions.
Some insurance companies have a program where if you have been claim free for a certain period of time then they will waive the first accident for you.
Another exception is based on a state's accident threshold.
Most states don't allow insurance companies to surcharge for an accident unless the amount paid by the insurance company is over a certain amount, such as $750.
Your policy should not be cancelled unless it was a major accident where someone died or where you were drunk, ran a red light, and then t-boned another car.
Then, more than likely your rates would be so high you wish your insurance company would cancel you because you couldn't afford it.
How about a claim where you were not at fault, how about a comprehensive claim like hitting a deer.
Even those these claims are coded as not at fault, if you have numerous claims - 3 or more - within a certain period of time - usually 3 years - then your rates could be affected.
Or if you are filing a bunch of small claims, your insurance company could force you to raise your deductibles or take the coverage away from you.