Moaboy is right. These are called "drive-away companies", and a Yellow Pages search should turn up many of them. They specialize in the retiree market, moving cars from New England to Florida and back, New England and the midwest to Arizona, and runs to California. I don't know how you separate the good ones from the fly-by-nighters, but make sure the one you choose is insured, and be sure to get a copy of the policy.
A full-service mover such a Mayflower Van Lines will ship anything, but tends to be expensive. There is an alternative kind of mover where you pack your own stuff and load it on the truck yourself, that is cheaper. They will ship anything, including vehicles, and partial loads are welcome. I'm not sure what they call these companies, but ABF U-Pak is an example. When I retired, we moved half our worldly possessions, including one car, from Maine to Arizona via ABF. The experience was not particularly good, but it worked.
Another alternative is an outfit dedicated to shipping antique and classic cars. There are a number of them - you see their big vans on the road occasionally. They tend to pamper the vehicles a bit, so they may be more expensive. But a search on "classic car transport" should turn up several.
Good luck.
Bill
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