Homeowners or renters insurance will reimburse the damage to your bike or if stolen usually on a replacement cost basis subject to the deductible. Don’t file a claim if the amount is near your deductible. You’ll lose your claim free credit and end up spending more in the long term.
Claims adjusters vary between companies. Some are helpful / some are looking for a way to screw you. If stolen, you usually need to provide some evidence of the theft. Save whatever is left of your lock. You need to specify a definitive time and place of the theft. If it’s just missing and you don’t know how or when, you’re screwed. It can even be helpful to get the name and number of somebody that knew you rode in on a bike and now its gone – somebody at school, work, a store, etc.
Don’t file a claim if it’s not your fault. The offending drivers auto insurance pays for the damage. Make sure you get the other persons insurance information. If you cause the accident, home / renters insurance will also pay for the other persons vehicle damage and/or injury under the liability coverage.
Auto insurance personal injury protection (“PIP” in some states, or “med expense” in other states) will pay for your injuries if you tangle with a vehicle. If you just biff on your own, your health insurance pays. If hit and run or the driver has no insurance, your uninsured / underinsured auto coverage will also pay for your injuries but (in most states) not your bike.