Am I liable for damages in an accident that involved a vehicle registered in my name but uninsured?

Yes, you could be liable. If the vehicle is registered in your name, you are the owner for legal purposes; the owner of a vehcle is responsible for any damage done by that vehicle, by himself/herself or by anyone else he/she allows to drive it. (Of course, you should only be responsible if the driver was at fault--that is, negligent, or careless; or else acting intentionally to harm another or another's property--in causing the accident.) The lack of insurance merely means that if you are found liable, you will have to pay the award or judgment yourself--there is no insurance to pay it for you. A lack of insurance does NOT prevent you from being liable.

As the registered owner of the vehicle, you are liable for the accident if you or someone else was driving your car and was at fault in the accident.

You are liable for the property damage to the other vehicle and the personal injury claims of the occupants of the other vehicle who were not at fault in the accident.  Property damage is the cost of repairs to the vehicle that was not at fault in the accident.  The personal injury claims of the party not at fault in the accident would include medical bills, pain and suffering (an amount in addition to the medical bills) and wage loss.

Since you did not have insurance, if there is a judgment against you in an amount you can't afford to pay, you might want to consider filing bankruptcy.  It would be premature to file bankruptcy until there is a judgment against you because at this point, you don't know the amount of the judgment.