What's the advantage of buying insurance from a broker instead of the insurance company itself?

I have car insurance through a broker right now and it’s very expensive. I have a feeling that if I shop around a bit I’ll be able to get a cheaper price directly from an insurance company or bank. However, would I be missing out on any level of service by doing that? If I get in an accident I would like to have someone knowledgeable who I can call right away to help me. Is that what a broker is for?