I am planning to move my laundry from the basement to the upstairs. I have heard that the front loading washers will rattle your plates off the shelf in spin cycle. Is this a common problem? Are there any solutions out there to correct this problem?

They sell(and you can make) rubber isolation blocks that you set the washer/dryer on which reduces vibration. You can find them in Lowe's or HD near the appliances. You can double this effect by using them between the washer/pedestal and pedestal/floor.

I made the pedestal that my washer and dryer sit on and fastened the shoe of the pedestal wall through the rubber isolation blocks into the floor, completely negating the vibrations.

Thanks,
Json

Json offers a good solution. When you move the washer make sure you have a 2" drain line to connect to or a laundry tub.