If you decide to move yourself without professional moving help, the trick is to start early and stay organized. You will want to begin packing as soon as you know you will be moving. Start by packing up all the breakages and getting them out of the way first.
If you hire a professional mover, and any of your items are damaged or broken, they are insured by the movers. The cost of moving yourself may be a lot more then the money you save if anything gets damaged.