You can stay on your parents health insurance until you reach 26 years of age.
Even if you don't live with your parents you can still be covered under your parents health insurance until you reach 26 years old.
Once you turn 26 years old you can no longer be on your parents health insurance and you have to get your own health insurance whether you live with your parents or not.
So in short you cannot stay on you parents health insurance after age 26.