The co-pay system is widely used in the insurance market as means for the insurer to protect themselves against customers who would file a myriad of claims with very low values. You, as an insured person, will have to pay a flat amount of money when you lodge a claim. Comprehensive and collision policies are subject to deductibles, and the amounts are agreed upon in the contract you have signed with the insurer.
Let's assume you have signed a collision policy with a $250 deductible. If you scratch your car against a fence while parking it and require a minor paint job of, let's say, $50, it would be pointless to file a claim, because you are going to pay the first $250 for all repairs. On the other hand, if you have more severe damages of, let's say, $1,000 then you will pay the first $250 and the insurer will provide the remaining $750.
Deductible amounts vary from one insurer to another. While there is no maximum amount (because it would highly depend on the model of the car and the insured value), minimums usually start at a few hundred dollars.
Some insurance companies allow the deductible to be waived, in certain conditions. With Esurance, for example, if you are hit by an uninsured motorist in some states, you can have the deductible waived. Here are some other scenarios where you don't have to pay the deductible:
A higher deductible would lower your premium, because it lowers the insurer's exposure to risk. The company would be paying you, on average, less money, so it makes sense that you are charged less. A lower premium, on the other hand, would limit your out of pocket expenses in the event of a claim. The rule of the thumb says that you should agree on a deductible that you could afford at any time, because you can never know when you are going to be involved in an accident.