Any repair that is put through an insurance company (yours or not) is going to show up on a Vehicle History Report VHR (i.e. CARFAX, AUTOCHECK) when you go to sell/trade. Because there will be an official record that your car was in an accident, you are going to get less for it, regardless on how minimal the damage was. You could lose anywhere from $250 - $1000 on your resale value because of this. Think about it, if you were going to buy a used car and you saw it had a collision you would expect a discount. However, if the repair is never processed through insurance, no one is the wiser and you retain your anticipated resale value.
The wild-card is if you do not go through insurance but there was a police report, it may or may not show up on the VHR. It really depends on how the police department process the paperwork.
It really all depends on the amount of damage (over the deductible no brainer get the insurance to cover it) and how long you plan on keeping the car. If you are a drive-it-till-it dies type of person, it would be worth getting the other insurance to cover it, because your hit will be minimal so far in the future. If you plan on trading it in in less than 5yrs you will want to weigh the options of: less money now, or less money later. If it is say a $900 repair it would be worth getting insurance to pay, because it will probably wash with the trade hit. But if it is a $300 repair it might be worth sucking it up so you don't get dinged $500 or more later.
Just wanted you to have all the options to make an informed decision.