I have talked about this before. It is even part of my presentation when I speak to high school students. What information do you need to get at the scene of an accident?
First, if the police come and separate you, do not push them on the issue. Let them do their job. While I believe you can still exchange information, if the officer says not to, then listen to the officer. They are in charge at the scene.
If the police do not come, or if there is a delay, you need to get some basic information. Start with the name and address of the other driver. This is going to be vital if you need to file a lawsuit at some point in time. If you can get a phone number, that would be great, but it is not required. If there are any passengers in the other car, ask for their names and addresses as well. This information is not required, but could be beneficial down the road.
After you get that information, get some basic information about the car. You should get the year, make and model. The license plate is also important, and I suggest people take a picture of the license plate so that they have it in the future, if they need it. Since I recommend taking pictures of the damage to both cars, this is just one more quick picture.
Then you should ask for the insurance card. If possible, take a picture of the card. If this is not possible, get the insured's name, which may be different than the driver, the name of the insurance company, and the policy number.
If you obtain this information, you are well on your way to making your claim a smoother event. This will help you and your attorney, should you need to hire one.