Now, that short, emphatic answer will need to be qualified in a bit, as you must be able to afford your car and continue making payments. But, as long as you can make the payments, you can keep a car in Chapter 7 and Chapter 13 bankruptcy.
The Bankruptcy Code is premised on the idea of giving debtors a "fresh start". This means giving bankruptcy filers the opportunity to go on with their lives and work as normal, and get back on their feet. Having a car is vital for many filers, so the Code protects their ability to keep their car. You need your car to go to work, pick up your kids from school, and run day-to-day errands. The law recognizes this, and makes it fairly easy to protect your vehicle.
The Federal bankruptcy exemptions allows debtors to protect $3,675 in equity for one car (two cars if the bankruptcy is a joint, marital filing). This $3,675 need only be applied to the amount of equity you possess, that is, the value of the car minus what is owed on it. Since cars depreciate so quickly, equity is normally quite small in a car. This is good news for bankruptcy purposes, as it allows most debtors to exempt their car.
A problem may arise if the debtor has multiple vehicles in their name. However, even this should not be an issue if the "wildcard" exemption is available to protect the second vehicle. The wildcard exemption can also be used if the automobile exemption is exhausted. An experienced bankruptcy attorney will be able to help you properly exemption plan.
The second issue in keeping your car is whether you can afford to continue making payments. When filing a Chapter 7 bankruptcy, you must be completely current on your payment at the time of filing if you wish to keep your car. Otherwise, the finance company can (and will) repossess the vehicle. If you are behind and want to file a Chapter 7 bankruptcy, it will normally be advisable to wait to file until after your payment is caught up. If you are behind on the payment and wish to abandon the car, Chapter 7 bankruptcy allows you to do so, while your obligation on the remaining payment will be dismissed. It is something to consider if your car payment is prohibitively high, or your car is a "lemon".
Chapter 13 bankruptcy allows you to not only keep your car if you are current on your payment, but also to catch up on arrears over the course of the bankruptcy plan. This is extremely important if your car payments are past-due and you are facing repossession. The Chapter 13 plan allows you to catch up over the course of the 3 to 5 year plan, and at its conclusion you will receive the title of the car. The Chapter 13 plan allows the arrears to be spread out over the full term of the plan, so even if you are multiple months behind, it is possible to catch up.
Misinformed debtors often believe they will lose their car in bankruptcy, but as long as it can be exempted (and it normally will be) and your payment is current, you can keep your car in bankruptcy.