The short answer to this question is Yes! You can stay on your parents' plan until you turn 26 regardless of which state you live in. You may, however for various reasons, want to look into obtaining your very own plan that is cost-effective and better suited for your new situation.
The Various reasons
The major drawback to being on your parents' health plan while living "out of State" or in a different state would have to be your access to in-network (and out-of-network) services.
Here, let me explain:
Healthcare in the United States is typically location-based. Your health insurance company will go to great lengths to build a network of local doctors and other healthcare providers to help make health and wellness services more easily accessible to their customers.
We see this type of tightly-built networks with Health Maintenance Organizations (HMO). With these types of plans, you will have a primary physician who will be in charge of ensuring access to cost-effective services by managing your access to other healthcare providers.
You will often have to receive authorization from your primary doctor before you can go see other providers, i.e. Specialists. Your "Primary" will ensure that you are seeing Specialists - by referral- that are in your network.
Accessing services outside your home State may cause services to become more expensive since you will be out of network and most out-of-network services tend to carry their own deductibles and other costs. Thus, leading to "surprise bills".
Considering all of these factors, it will often make more sense to sign up for your own health insurance plan if and when you move away from your home State. Especially if your move is a permanent one.