I just had my '66 Plymouth Fury VIP shipped from South Carolina to here in California so I have recent experience.
I used Anytime Auto Transport. I was very saftisfied. I called on a Wedneday to set up shipping. I said that the seller of the car won't be at home Friday and Saturday, so any other day would be okay for pickup. They said it could be picked up on the following Monday but called me back a few hours later and said they could pick it up on Friday of the same week!
They estimated shipping would take approximately 5 days; it was delivered on the morning of the 6th day.
Website is
http://www.aaaanytime.comCheck out the "about us" page. They give warnings on what to look for when choosing a shipping company. Including some that will park a car being transported at a terminal for several days. Mine was on the truck the entire time. They use two drivers which is how they can ship cars coast to coast in less than one week.
I highly recommend this company and it has an A- rating from the BBB.
Here are a few photos I took of the car still on the carrier moments after it arrived at my house...