A common feature of moving companies is that they all have lists of items that they will not allow onto their trucks. Given that you're likely not going to pack anything that's plugged into a power source or that includes open flame, the restrictions might seem unnecessarily strict in some cases. However, there is logic behind the restrictions. If you are planning a move and want to pack things that the moving company refuses to take, it's likely that the items are either susceptible to damage and able to cause harm because of conditions during the move itself, or the state you're moving to prohibits the items.
One example of a state not letting an item in is plants. States have agricultural restrictions that prohibit certain plants or types of plants from being brought in. The logic behind this is that the plants could harbor diseases or pests that could damage crops in the new state.
For example, if you've been growing onions or garlic in containers and want to take those containers with you when you move to Idaho, you can't. Not only is there a spill risk -- if the container overturns in the truck and the box the container is in breaks open, the soil can spill everywhere -- but there's a state restriction due to disease. The risk is that the onions or garlic contain the white rot fungus, which is a major threat to crops in Idaho (home gardeners in Idaho can't even plant garlic or onions that they bought from a supermarket there -- they have to order special certified-disease-free slips).
And if you're moving to California, you can't bring in citrus trees because of the risk of bringing in four different diseases that could devastate the California citrus industry. Try to bring those in, and agricultural inspectors will destroy the trees. They could also possibly fine the moving company.
Flammability and Fire or Chemical Risks
Another issue is the heat that can build inside a moving truck as your goods are being transported. If you want to move a bunch of household cleaners that you got on sale, for example, the heat inside the truck can cause the internal pressure of some of the cans, such as spray disinfectants, to increase to the point where they explode.
Other times it's not materials on or in the item itself, but what those materials could do if something else explodes or is set on fire. Matches alone seem harmless, but if something ignites in the truck, and the flames reach the matches, the fire can become so much worse because of the sparks from the match heads as they ignite.
And sometimes it's just the risk of a mess. A candle with a regular twine-like wick seems about as risky as paper or clothing, but the melting wax in the heat can result in leaking boxes that let melted wax and oils out onto the truck floor. Plus, if the candles are scented, everything in the truck is going to stink. You might like the scent, but the driver might not, nor would future customers whose belongings could pick up the scent after the wax is cleaned out.
If you're still confused about why certain items are prohibited, you can always call the moving company, such as http://www.bekins.com, to find out any restrictions. You won't be able to negotiate to ship the items, but you'll be able to get a better understanding of why moving some items can be a bad idea.