Tamra,

First of all if your move is long distance one, I would suggest you to empty all your drawers and pack everything in boxes. They have a long way to go and will be moved from place to place many times before reaching your new home.

For local moves some things could easily be left in drawers (like linen), so when movers put moving blankets on top of the drawer and hold them in place with tapes nothing wrong should happen with it.

Things like office tools and supplies should be taken out of desks, because you don't want them to get all mixed up by the time your furniture arrives at the destination.