When you get married, how do you get off of your parent's insurance, etc?

My dad still has me declared as a dependant, and my car insurance and health insurance is on his. When I get married will these automatically change, or do I have to notify the insurance companies and tax people?

It won't change automatically. You will have to change your last name with the social security office, the DMV, your bank, credit cards, insurance agents, etc.. It can actually be very time consuming. Once you are married you can enroll on your husbands health insurance through his work (assuming he has it), it would be considered a qualifying event, so you shouldn't have to wait for open enrollment (but it may be different depending on the place that he works and their benefits). As for taxes, once you are married, your father shouldn't be claiming you anymore and you will now most likely file as 'married filing jointly'. Same goes for car insurance. Is the car in his name only? If so, then his name has to be on the insurance. If you are a additional driver on HIS policy then he can have your name taken off and then you get your new policy in your own name (and your husbands, if he too will be driving the car).
So anyway, it's a lot of work once you get married (and take someone else's last name). But as I said before, nothing is done automatically for you. There are a lot of phone calls and paperwork involved.

You don't have to notify anyone. Your parents will drop you from their insurance once you get insurance on your own. If you do this with the same company, like State Farm, get your dad to come with you when you sign the paperwork and you can be dropped from his at the same time. As for taxes, your dad has the power to claim or not claim you during tax season. Just tell him that you want to file jointly with your spouse and not to claim you. You should be fine after that.

Both need to be notified. Health insurance coverages ends for you the day you are no longer a dependent, which is the day you get married. If you fail to notify them then they may continue to charge him premiums for coverage that really doesn't have. Also if you fail to let them know and they process a claim for coverage after your marriage you can be held for insurance fraud.

Nothing automatically changes upon marrying notify the insurance companies & social security admin if you change your name. If your dad will continue to provide over 50% of you or your spouses living expenses he can still claim on your taxes. Otherwise, you and your spouse will file your taxes together next year.