Staying onsite is really nice, as long as all you want to do is Disney. If you want to do anything off property, then you truly do need a car. There are public buses, but to use them efficiently, you need to have a schedule and a route map. Taxis are always available,but you have to be truly on your toes. They'll rip you off at the drop of a hat.
To rent a car you have to be 25 years old. There used to be an exception to that but it was hideously expensive. I don't think they do it anymore.
So! Hope that helps a bit!