Yes. Just because you are young and healthy does not meant that you do not need health insurance. You can opt for a policy with a high deductible, say $2500 or more, but everybody should have some type of health insurance.
There are many unanticipated health insurance costs, such as a broken ankle, or finger that can cost $10,000 or more. You will be required to pay this bill, even if it takes time. It will not just go away.
You are not just endangering your own financial well being by not carrying health insurance, but your entire family. Should you come down with a major disease, such as cancer or any chronic life threatening disease, your parents would most likely pay. They may have to decimate their entire savings, however, to afford this. Many major medical treatments can go in to the hundreds of thousands of dollars to cure.
Also, for a young, healthy person, health insurance is not expensive. It can be just a couple of hundred of dollars per month, or less, especially with a high deductible. This can be easily afforded by just skipping a night out. All people, even the young and healthy, should carry health insurance.