I've used two companies I would recommend...
Reliable Transport has moved three cars for me. One from GA to CA, one from Alabama to CA and one from CA to Missouri. Two of the cars arrived ahead of schedule, and one right on time after only two days transport time. All were delivered by husband / wife teams who were car nuts. I saw great attention paid to the safety and well-being of the cars during transport and unloading, and I have high expectations.
http://www.reliable-carriers.com/
The other outfit was TFX International. They were very friendly and the driver was a great guy. The car did arrive a day late but it wasn't their fault. Seems the delivery before me said there was room to turn the truck around, but when the driver got there it was a very narrow road. So he had to back the truck down a twisty mountain road..... for 20 miles!! He got extra points for calling my MG YB "the cat's meow".
http://www.tfxinternational.com/
Another company I've heard spoken highly of is Horseless Carriage. They specialize in collector and exotic cars. Their prices are a bit higher than others from what I've seen but I have no personal experience with them.
http://www.horselesscarriage.com/
When you choose a transport company, I recommend avoiding brokers. They are just a middle man, so you could pay more for transport and you won't even know who is actually moving the car for you. Using one to move your car is taking a chance. Sometimes it works out well and other times it becomes a nightmare. You need to decide how much of a risk you're willing to take, and how much money that risk is worth to you. Ask if they own their own trucks, and ask if it is enclosed or open trailer. Open is cheaper but will not protect the car from weather, rock chips, etc.
Hope this helps!