When I moved from Atlanta to Seattle back in 2003, I had my car shipped here. It ran about $1200 bucks, if I remember correctly, and it took about two weeks (of course, I was shipping it over the holidays, so that was the main factor for it taking so long).
I got into Seattle on January 6, and my car came in two hours after me. No problems whatsoever, outside of the fact that it was FILTHY. But the guy who was driving the truck gave me 50 bucks to have the outside AND the inside cleaned. I'd definitely do it again.
The only real piece of advice I have to offer is make sure all your valuables are locked away (I *did* lose the change from my cup holder, but that was only a couple of bucks), and don't try to pack the car full of stuff. Most carriers won't let you do that anyway. Also make sure you arrange to pick up/drop off your car in a large area, like a supermarket shopping lot, because they'll need the room.