A recent study by insurancequotes.com shows that your auto policy rates can go up when you make a claim. In Missouri the rate increase is about 27.5% with Illinois increasing at 29.4%. These are on the low end of the scale. In Massachusetts the rate increase averages 67.4%.
This is usually for at fault accidents resulting in property damage and/or bodily injury. According to the article, it makes it more risky for the insurance company to cover you after an at fault claim. These increases usually last approximately three years.
If the damage is close to your deductible it would make more sense to not make a claim admitting fault.