Plants pose a unique challenge in the moving biz. 

Drivers may take plants, but are sometimes reluctant to do so due to the space they take up (considerable due to inability to stack anything above them), relative to the weight they add (minor).  Whatever you do, don't count on them being watered by the driver. 

Another factor to consider is that even if the driver does accept your plants as part of the shipment, should his trailer be inspected along the way (i.e. at state weighing stations, etc..) he may be forced to offload the plants, should he be ordered to do so by officiials.

California is particularly tough in this regard.  Most states try to protect their crops/plants from being infested with insects from other states, even if the plants are just passing through.

My suggestion is this.  If you have small houseplants, give them to friends or relatives prior to your move.  If you have larger plants that you want to take a chance with, pack them in boxes and hope for the best at the weigh stations/checkpoints.  Since they're not going to be watered anyway...what do you have to lose?  For tall plants, I'd suggest a wardrobe box.