After you get in a car accident, you might not be thinking too much about onlookers. However, if everyone directly involved in an accident has their own ideas of what went on, outside witnesses can really come in handy.
Witnesses who are uninvolved in an incident usually better provide objective accounts of that incident -- the actual participants may be more limited (or biased). For starters, witnesses are usually in a better physical position to report what occurred -- it's easier to see what's happening if you're not in one of the cars involved in an accident. Most witnesses also don't have a personal investment in the outcome of the situation and may provide a unique and balanced perspective. They can also help identify patterns and causes in an accident: If this is the fourth crash Joe Onlooker has seen at a certain intersection, for example, that's important information for your insurance company to look into.
While many car accidents are resolved amicably, it never hurts to be prepared with the facts in case things turn ugly. Before leaving the scene of the crash, exchange names and contact information with any witnesses in case you or your insurance company needs any corroborating evidence down the road.