In the States, car insurance follows the car, not the driver.
If someone steals your brother's car and smashes it into a school bus full of children, your brother's insurance would be liable. Granted they'd likely try to pursue the car thief for the damages, but if he was stealing the car, the insurance company wouldn't be able to get very much from the thief. They may decide to drop your brother when the realized that the keys were left in the ignition...
Similarly, if you have permission to drive his car, and something were to happen, his insurance company would cover damages to the other party (basic liability). His insurance may not cover damages to his car, or your medical needs, and the minimum requirements vary widly by state. (you didn't state what kind of insurance he had, e.g. liability, collision, comprehensive, personal injury, etc.)
You and he should have a talk about his coverages, and make sure you are both happy with his currently liability limits. (i.e. If he only has $50K liability coverage and you total someone's $60K Mercedes with $20K in medical bills, and the other guy gets a rental car for 2 months, then you may be sued for the difference)
If he didn't add you to the policy and something happened, they would probably pay the claim, and then say "hey, why was someone else driving your car?", and then jack up his rates for a few years or even drop his [future] coverage, and he'd be out looking for a new insurance provider.
Ultimately, you and he should review his coverage, and the terms regarding how and when additional members of the household should be added.
Additionally, I think every person should review their insurance every 2-3 years or so and shop around to prevent rate creep.