Car Battery

If you are having a moving company transport your belongings, it should provide you with a list of "non-allowables." This is an industry term for items professional movers will not transport.
This list not only includes no-brainers such as ammunition and gasoline, but also seemingly innocuous items like nail polish and kids' chemistry sets. Although not hazardous, the moving company will also include perishable food and personal or sentimental items.

Hazardous material

You may be surprised to see some of the items listed as hazardous, but there are usually good reasons to have them included. Fertilizer, for example, can become highly explosive under the right circumstances. This was the primary component used by Timothy McVeigh in the Oklahoma City bombing that killed 168 and injured 800 in 1995.
Many of these items can be given to friends and family. Unwanted items will have to be disposed of properly. Contact your city or county for where to dispose of these items.
Hazardous items are generally those considered explosive, flammable or corrosive. Here's a list of common items that moving companies consider non-allowable:
AcidsFire extinguisherNail polish remover
AerosolsFireworksPaint thinner
AmmoniaGasolinePaints
AmmunitionHousehold batteriesPesticides
Car batteriesKerosenePoisons
CharcoalLamp oilPool chemicals
Charcoal lighter fluidLiquid bleachPropane tanks
Chemistry setsLoaded gunsReloading supplies
Cleaning solventsMatchesSCUBA tanks
Darkroom chemicalsMotor oilSterno
FertilizerNail polishWeed killer

Perishables

With long-distance moving, food items will not be allowed by movers. This is because the food will not keep and could attract rats and other pests that might damage your property.
If your move will be picked up and delivered within 24 hours, the moving company may allow perishables to be transported as long as they are properly packed.
Perishable items include those listed below.
Frozen foodRefrigerated foodProduce
Opened food productsPlants, including indoor 

Personal or sentimental items

Professional movers don't like to transport these items because of the inherent risk of loss or damage. Basically, movers want to limit their liability in case these items are lost or damaged. As a consumer, you likely want to have these items under your control anyway.
The loss of medical records, financial documents or school records could be difficult to replace. Sensitive electronics, such as laptops, might be damaged by the extreme temperatures in a moving van. Jewelry, cash, collections and personal video tapes or CDs could not be replaced if lost.
Here's a look at what moving companies consider personal or sentimental.
Address bookComputer discsPersonal video tapes, DVDs
Airline ticketsFinancial documentsPhotographs, photo albums
Car keysInsurance policiesProfessional files
Car titlesIRAs, deeds, tax recordsResearch projects
CashJewelrySchool records
CDsKeys to furn., safe, homeSterling silver
Cell phonesLaptop computersStocks or bonds
Certificates of DepositMedical, dental recordsWedding albums
CheckbooksMedicine
Collections (coin, etc.)Pagers