*Most* insurance companies will only cover dependents. So your parents would have to be able to claim your exemption in order to maintain insurance coverage for you.
There are several conditions that have to be met in order for them to be able to claim you. You meet the relationship and age tests since you are their child, under 24 and a full time student. The only issue I see is your income. In order to claim you as a dependent, your parents would have had to have provided more than half of your support for the year.
If you provided more than half of your own support, you get your own dependency exemption, but you'll most likely lose the insurance.