More than a few people I know have told me horror stories about moving companies ripping them off when they've moved to a new house or apartment. Their stories are similar: the moving company loads your stuff on the truck(s) and then it tells you to pay a lot more money than the written estimate. Movingscam.com is an information clearing house about moving company scammers, with tips for finding honest movers.
One thing I should point out, is that the bids from these companies that I have seen often quote you by cubic footage not by weight. If you get a quote that is priced by cubic footage, that should raise a red flag right away. The reason for this is that if they charge you by weight, they have to provide proof of the weight of your belongings at no charge to you. Current laws regarding the moving industry do not cover moves based on cubic feet.
Once the movers show up and most or all of your things are in their truck, they will hit you with the real price of the move. By then it's too late. Your things are on their truck, and they won't get anything off of it without full payment in cash. They will tell you that if you don't pay up, that they will take the truck and sell everything you own to cover the contract. In my case, I put down a $150 deposit, and was told before the movers showed up that the rest of the $1869 would be due on delivery. When the movers showed up, the price jumped to $5012.50, and the movers demanded half of that on the spot or else there wouldn't be a delivery!
Link(via Sensible Erection)