One caveat to those of you who shop around- be careful that you're aware of any differences in coverage. In the old days, most insurers used standard coverage forms developed by Insurance Services Office (ISO) so if you went from Company A to Company B and your deductibles and limits didn't change, you knew that the same things were covered.
A few years ago, I read an article in a CPCU (Chartered Property and Casualty Underwriter) newsletter pointing out that the cheaper insurers were chiseling away at little bits of coverage, that typically no one would notice- until they filed a claim. They cited a case where Person A was the policyholder, they rented a car, they let Person B (who apparently had no insurance or insufficient insurance) drive it. Person B caused an accident. The plaintiff went after Person A, who was not covered because the policy didn't extend to rental cars the insured loaned out to someone. The ISO form would have protected Person A. If it's Homeowners coverage, they may be quoting a policy which gives you only the depreciated value for your roof rather than replacement value. You may not care, but at the very least you need to know if you're getting a lower quote because you have less coverage rather than because the previous company was gouging you.
One other example: I got a lower quote for Homeowners coverage so I switched. They then did a re-appraisal of the replacement value of the home, came up with an insane number, and increased my premium- to what I'd been paying the previous insurer.
I'm a retired property-casualty actuary and I still prefer to work with an agent who knows what he/she is doing.