You can either trade or sell the car. I would prefer to sell the old car if I can get a good price for it. Also, if they car doesn't work anymore for some reason you can take it to a junk yard and get some money for it. People are always looking to get used parts.
They trade it in, sell it, keep it, or give it to their son/daughter for when they start to drive. You save money that way.
Name something.. Hmm.. People normally sell their old ones away I suppose? Or have traded it for a lower price on a new car. If the car is no longer road-worthy, it is normally scrapped.