Yes all insurance companies do run your credit to see if you're a good risk or not.
Your credit score is used to assign you an insurance score and if your credit score is low or bad then you'll likely have higher car insurance rates and in some cases if it's health insurance, life insurance etc then you may be denied coverage for insurance especially Homeowners Insurance if you have bad credit.
You can still get car insurance though with bad credit but your rates will usually be a bit higher.
Credit Scores are a good indicator of your financial stability and credibility.