if you were rear-ended it's likely going to be ruled not your fault and so it's the other party's insurance that will pay. Unless you live in a no-fault state.
If you have comprehensive insurance than by all means file a claim against your OWN insurance if you do NOT live in a no-fault state. The reason is that your own insurance company will simply claim it against the other drivers insurance company and so they will not lose any money, thus they have no incentive to fight down the cost of repair. And your rates will not go up because blame will be assigned to the other driver.
If you have collision only then you can't claim against your own insurance they won't allow it. So instead you have to file a claim with the other company and this is where it can get ugly. They have a big incentive to not pay out. So they will argue over everything.
What you want to do in those cases is the following:
1) DON'T allow their insurance adjuster anywhere near your car until AFTER you have obtained estimates and given the high-bid ones to the insurance company. He will just write a rediculously low estimate and then they will stonewall and refuse to pay you anything higher. If you get the estimates first and then he writes a lowball estimate then it looks like they are trying to cheat you so you have a basis to argue from. if you can, don't let an insurance company adjuster near your car.
2) Go to the most expensive body shop in the city, the one that fixes the rich people's cars. There are likely 2-3 of those places. Get estimates from 3 of them. And also, make absolutely sure that they include parts scavenging labor. In some of these cases the parts are no longer available from the dealership or the aftermarket because the car is older, they are only available from a wrecker. I've had body shops give me book estimates for parts costs, then I make them call the place they would get the bumper or whatever from and they find out it's discontinued. So I then say "well WTF are you going to do if I tell you to repair the car" and get a bunch of mealymouth rubbish about how they will have to call around to wreckers and so on. In other words, they will have to spend hours of time sourcing a part from halfway across the country and of course they are going to charge a lot of extra for that. Make them put that extra time on the estimate.
3) Ask what body shop the other insurance company suggests and make a point of not going within a mile of it.
4) Make sure all police reports are filled out and filed immediately. List every possible bit of damage on the report. Also if you got ANY kind of medical injury - even a minor bruise, head got banged, whatever - put it in the report, even if you didn't go to the hospital.
5) Refuse to allow them to pay the body shop directly. If you are collission only and are filing a claim against the other drivers insurance, that insurance company cannot force you to accept a payment to a body shop.
6) DON'T allow them to total out the car. Find out the blue book of the car and take a payment at least $50 to $100 UNDER the blue book in order to prevent the car from being totaled. If they total it then your title is branded salvage and then the car becomes worthless even if you fix everything.
Insurance co's greatly prefer to total out cars because they know that once they total a car the driver will never be able to file a claim against them for further damage to the car again.
Insurance companies also have sweetheart deals with certain body shops in the city. There are body shops that are experts at cutting corners and just getting the car to LOOK ok but the damage isn't actually fixed, they do stuff like not hammering the dent out completely so you get inch thick layers of bondo, sanding and painting over rust instead of burning it out, buying very cheap aftermarket body parts that don't fit so well, and so on. If an insurance company that is liable for a claim is able to they will "steer" you to one of those shops for an estimate.
Also keep in mind the Insurance company's primary goal is to close the claim. Many will issue you a check only on condition that the check closes the claim. Once the claim has closed then you cannot add to it. So if in fact there IS any medical issues, you may need to pay the medical bills yourself and keep the claim open as long as your state allows it. In some states were people buy collision only they still have to buy personal injury protection and so you always claim medical against your own insurance regardless of who is at fault.
Anytime you get hit in a car, even if you feel fine, you should always complain loudly to witnesses and the other driver that your hurt or feeling sore. Of course don't overdo it because the last thing you want is some do-gooder calling an ambulance. But none of those witnesses will be helping you to argue against the insurance company weeks later and it's really none of their business whether you got injured in the accident or not, so you do not want them saying "he looked fine to me" if they get asked. And if a medical claim is ever involved believe me they will be asked.
Lastly, you gain an advantage to sound as stupid and dumb as possible. Insist on getting the check cut to you directly and when they ask, instead of telling them something reasonable, tell them that your aunt matildia got screwed over once when she got in an accident and the insurance company told her they were paying the body shop directly but didn't. In other words you want them believing that they will be arguing with a body shop over the price of the repair, and your just the proxy. If they think for a minute that your educated enough to do your own repair then they know that the entire thing is a giant game and all you want to do is profit from the repair and then they will have no qualms about fighting the price down.
Your time is worth something. You have had a lot of it wasted already, you wasted it when you had to stop and exchange info after the accident, your going to waste more by hauling your car around for estimates, etc. No matter how you slice it this is a financial loss to you that morally, the other driver (and by proxy his insurance company) owes you. Thus, do not feel the slighest qualm about pulling every trick in the book to jack the estimate for repair up as high as possible, no matter how high you get it, it won't make up for the total financial loss you take.