In general it depends upon your insurance company's guidelines and the state laws of where you are a resident and the state where you are attending school that dictates where you should have your insurance.
Normally if you are a student attending school out of state you will need to discuss your auto insurance policy with your agent to see if your coverage will extend to you while you are out of state at college. Some insurance companies will allow you to keep your policy and coverages in place while you go to college, while other insurance providers will not either due to the distance from your home state, the different insurance requirements in each state and / or due to the fact your car will be garaged and driven out of state for an extending period of time.
In some states even if you are a student attending University or College, you still will need to comply with their in state insurance requirements. For example, according to Florida statutes any person who has a vehicle in Florida for more than 90 days during a 365 day period (the days do not need to be consecutive) must purchase personal injury protection and property damage liability insurance coverage.
Another example is in Louisiana. If you are a LA resident but going to school in Texas keeping your current auto insurance may be a problem, depending on your insurance company. If the company is licensed to do business in Texas then you should be able to stay with that company however the Louisiana Insurance Commissioner states it would be up to the guidelines of your individual insurance carrier if they would continue your policy or drop you so that you would obtain TX insurance.
So to determine which state to register and insure you car, first try speaking to your current insurance agent to see if your policy will follow you. If it will not then you will need to get insurance in the state where your college is located. If your insurance will cover you then you may still want to see if it is possible or required to insure you car in the state you are attending school in. A call to that state's Department of Motor Vehicles and/or insurance regulator should provide you with the information you need.