I have used Western Carriers twice. They advertise in Wine Spectator every month in the advertisement section. They are fantastic, and I insisted on using them again when I recently moved from Houston to LA. Joel Rubens is the guy to call. He is very responsive to his email, and offered to hold my wine for a month for free in a refrigerated warehouse until I was established in our new home and had leased new offsite storage space.
Everything gets shipped in climate controlled trucks from point A to point B. Prices are very reasonable. All of the points that Rob brings up are true. If you have no insurance, and you want them to insure it, it is expensive. I already had wine coverage, through my home insurance, and so every bottle was covered during the move, and so I did not need to pay for this extra premium. They will package the wine for you (extra costs) or you can do it yourself. I did it myself so that I could track where every bottle was located. Shipping wine in those bulky boxes with styrofoam will cost you more - prices are based on not only the number of boxes, but also the number of pallets they need to hold your wine (space). Smaller, space-efficient boxes without the styrofoam is the way to go for shipping purposes.