I've been meaning to write this for a while but never got around to it. Some comments in the crumpled Speedvagen thread finally gave me the nudge. Hopefully other lawyers or industry folks will chime in and make this wiki-worthy.
In case you get hit and find yourself in the position of having to deal with a driver's insurance company, here are a couple of hopefully-useful tidbits:
In most cases, there are two separate claims: a property claim and an injury claim.
Settlement of the property claim is usually pretty cut and dried -- your bike, helmet, clothes, etc. cost what they cost -- and can be resolved within a few days. Make sure that, in getting the check for your bike, you don't inadvertently settle your injury claim as well.
In general, run-of-the mill injury claims are settled for some multiple of the total cost of your medical bills -- typically 2-4 times your medical bills around here (and that's the full-ticket self-pay cost, not the discounted rate your health insurer negotiated). The amount above your medical bills is there as compensation for damages like pain and suffering. If you are in an accident that hospitalizes you or causes you to miss work for any period of time, call an attorney and don't try to handle the claim yourself. In 90% of cases, you will come out better in the long run.
If you are ever hit by a car, go to the hospital. Period. Beyond just making good sense health-wise, it makes settling your injury claim much easier (and, let's be honest, more remunerative). Don't try to be tough and for God's sake don't try to save the driver's insurance company money. The driver hit you, so he deserves to pay to get you checked out. Even if you're not seriously injured, the driver's insurance company is still on the hook for your ER visit, so go. If nothing is required past the initial ER visit, once you get your bill, then you can call their adjuster and start negotiating. They do this a lot, so the best advice I can give you is pick a reasonable multiplier (2.5-3x medical costs) and be stubborn about it. Don't worry if you don't get it settled on the first call. If further treatment is required, wait until it's completed before you start negotiating, so you have a complete idea of your medical costs. Time is of the essence, though, since personal injury statutes of limitation tend to be short -- one year in many cases. If your medical treatment is extensive, call an attorney.
Once you settle your injury claim, you probably owe some people some money. (It's called a right of subrogation, if anyone cares.) If your health insurer paid for your trip to the ER (or subsequent medical expenses) you'll need to repay them. If the hospital bill is still unpaid, you'll need to pay that. In either situation, it is frequently the case that you can negotiate a reduction in what you actually pay. Most hospitals, in particular, will knock off 30% in the first sixty seconds of your phone call. Make it clear that you've got the cash in hand and will send them a check today, since medical collectors are very much in the "bird in the hand" business. Be aware that a single trip to the ER can generate multiple bills -- one from the hospital itself, one from the treating physician's group, and one from the radiologist's group (assuming you have an x-ray). Make sure you have them all before you total up the numbers.
Other lawyers can feel free to chime in and correct me. And here's the ubiquitous disclaimer on behalf of myself and any other lawyer who might contribute: We're lawyers, but we're not your lawyers, and we're almost certainly not licensed in your jurisdiction. Anything we say is provided as general information, and is not advice for the handling of your particular case. Seek professional counsel.