I shopped around for car insurance a few years ago, and found that Liberty Mutual was the only company that undercut my policy with Allstate. I also checked with Progressive and Geico, both of which were nearly double what I was paying at the time.
So I
attempted to switch.
I paid for a policy with LM, and after five weeks, had not received any documentation. By that point, having made several phone calls over the previous few weeks and receiving nothing but lame excuses, I canceled the policy and demanded a refund.
I got it, but it took a while. Quite a contrast to the fifteen seconds it took them to deduct my initial payment from my checking account.
In retrospect, the lower price (only $30 less per month for three vehicles on full coverage) wasn't worth taking a risk on a company whose reputation and customer service were unknown to me.
Allstate is a great company with reasonable rates and good customer service, so I am staying put.