What moving company you use depends on the level of service you require. There are a number of places, like Uhaul and Penske, where you can rent trucks, trailers, and packing supplies and do the packing, loading, and driving yourself.
The next level of service is the "you pack it, they ship it" model. Companies will large tractor-trailers will rent you square footage in a truck that is already making a trip. You may get 15 linear feet of space on the truck floor, and share the truck with two or three other renters.
The full service moving companies also give you choices. You can pack your own items with these companies too. Or, you can pay extra for the company to use their own boxes and labor to pack your items. This is a good way to go if you can afford it, because then the safety of your items is insured and the company will have to reimburse you the value if an item is damaged in transit.
Whatever you do, plan early. The easiest way to get the mover you want, or get a truck to do it yourself is to make reservations a month or so in advance.
If you are moving in town, you can find the right companies in your yellow pages. If you are moving out of town, you can find national companies on the Web.