Getting into an auto accident is stressful, even if no one is injured. Don't put yourself in a position to be even more stressed out because your accident occurs on a Saturday night, but your insurer doesn't open for business until Monday morning. Plenty of insurance companies now offer 24/7 claim reporting, both by phone (toll-free number) and online, so make sure you select one that does.
Ask, too, if there are any special requirements when filing a claim. In general, you just have to give your name and address, the names and addresses of anyone injured in the accident or who witnessed it, and general information about the nature of the loss or claim. It also helps to have your policy number on hand.