Simone,

It could be a problem if you are moving long distance. First of all you need to call your local U.S. Department of Agriculture to check on regulations if moving from one state to another. Many states have restrictions on certain kinds of plants to prevent importing bugs or pests that can destroy valuable cash crops in that state. I know California and Hawaii are especially strict with that.

Second, most moving companies will not take your plants in the moving van, as there is little chance they will survive. There are no temperature controls in a moving van, and temperature changes may be extreme. In addition, the plants will not be watered, or receive any sunlight, from the time they leave until the time they arrive.

Should a mover allow your plants to be loaded with the rest of your belongings - it will be at your own risk.

If you are moving locally I would recommend you to read those tips to learn how to ensure your plan survive the move:

http://www.movingatoz.com/MovingGuide/Chapters/pet-moving-tips-p2.php#B5