Dressers and the like are not designed to be moved full, but whether you can leave clothes in the drawers depends on the moving company.

Some will say you can keep your clothes in the drawers for a local move (but they should just be clothes so you don't make the dresser overly heavy). For long distance moving, these movers will generally want the clothes packed in boxes.

Other moving companies will ask you to empty the drawers no matter the distance because of the potential for damage -- to the furniture because of the strain on it, and to surrounding items because the dresser will be more difficult for the movers to maneuver.

Even if your moving company permits you to keep clothes in your drawers, if you value your dressers, you should remove everything just to be safe.

Related topics:

Packing Large Pictures and Furniture

Moving, Storing and Insuring Expensive Furniture