Downsize Before You Move
If you don't use it, lose it.
You know that treadmill you've been using as a drying rack? It'll be cheaper to get rid of it now than it is to ditch it when you arrive at your new place. Movers base their prices on the amount of stuff you're shipping, so cutting down on the clutter will simplify your life and lighten up the load in your moving truck.
Start packing a few weeks in advance, keeping only what you use. Be realistic: If you haven't used your bread machine in over a year, you probably won't miss it. Sell those extra possessions online or at a yard sale, or donate them to charity. You'll save money during the move and coat your pockets with a little extra cash for unexpected moving expenses.