You can take your plants with you when you move without harming them.
Here are some tips.

 Call the 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 and/or pests that can destroy valuable cash crops in that state.

A couple of weeks before you move, prune plants to facilitate packing. Consult a florist or plant book for instructions.

A week before you move, place a bug/pest strip, conventional flea collar, or bug powder in a black plastic bad; then, put the plant in the bag. Close the bag and place in cool area overnight. This will kill any pests on the plant or in the soil.

The day before you move, place the plants in cardboard containers. Make sure they are held in place by dampened newspaper or packing paper. Use paper to cushion the leaves and place a final layer of web paper on top to keep them moist. Water the plants normally in summer, a little less in winter.

On the day of your move, set the boxes aside and mark "DO NOT LOAD" so they will not be taken on the moving van.

On the day you leave, close the boxes, punch air holed in the top, and load in your vehicle.

When on the road, be careful where you park your vehicle. Look for a shaded area in the summer and a sunny spot in the winter.

Unpack the plants as soon as you can after arriving. Remove plants through the bottom of the box in order to avoid breaking their stems. Do not expose the plants to much sunlight at first. Let them get accustomed to more light gradually.

If you must leave your plants behind, then take cuttings. Put them in a plastic bad with wet paper towels around them.