Avoid moving companies that can't provide an address or license information. Ask if they have marked trucks and use a moving company that does. Never hire a company that depends solely on a budget over the phone or online, or that requires a large deposit. Many moving companies will call to confirm the time and address of the move a few days in advance, but if they don't, call them yourself and make sure nothing has changed.
The moving industry doesn't have the best picture: most of us have heard of a move that went very wrong. Even if you book your move with them, they are not responsible when something goes wrong because you actually have a contract with the moving company. You may also have to pay two bills at the end of the move: one for the moving company and one for the moving agent. Moves are generally billed according to the weight of your belongings (using a volume-based formula) or according to the length of the move.
Make sure that your moving company provides you with a manual of consumer rights and responsibilities before the move begins. Choosing a moving company that checks the background of all its employees will go a long way in ensuring your safety during the move.