Yes, you can still trade in a car that has negative equity (i.e., you owe more than it's worth) through your dealer. When you trade in a car with negative equity, your dealer uses an "upside-down" or "rollover" loan:
Upside-down: You finance what you still owe on your old car into your loan for your new car.
Rollover: Rollover is what dealers usually call an upside-down loan.
