Only one answer really addressed the question, but I will add to it. Having worked in auto industry a bit, being a car guy, and with friends in the insurance business, here is the deal:
It ABSOLUTELY reduces the value having been in an accident. The newer the car, the worse it is. When trading in a car, the first thing a dealer looks for is paint work. Any sign of repaired damage (even repaired well) drops the bottom line. In a private sale, people will generally ask rather than be able to deduce it themselves, although accident reporting to carfax is changing that. If they do not and it is repaired well, and you do not tell them, it would not make a difference, but that is not my style.
Now how much and if you can do anything about it is debatable. It depends greatly on the amount of damage, how well it was fixed, and year/make/miles/condition of the car otherwise. And therein lies the problem. There is no way to calculate it and so no way to prove it to an insurance company. They will generally fight giving any depreciated value, usually successfully. This is your only chance though. You must get the money then prior to any damages agreement and settling the claim. Once settled, you are out of luck. The way I would go about proving it is by taking it to 2-3 dealers and getting a trade in value, then asking how much teh accident affected it. The number you get will be on the high side since they try to get the car as cheap as possible using any justification to do so.