It is not just paper that has sensitive information. Your hard drives also need to be destroyed before they leave your possession. This is required for compliance with federal and California privacy laws including HIPAA. Just deleting files is not sufficient to destroy the information. It is easily recovered with free software.
To be sure the information is destroyed there is no better way than to physically destroy the hard drive. Hard drive destruction can be done on site or at a secure plant. The pieces are then melted down for metal recycling. This is absolute destruction.
Don't forget all of the hidden hard drives in your office. Copy machines and fax machines also have hard drives that must be shredded before they are sent off to the Oakland recyclers. These drives store digital images of what has been scanned and can be recovered easily.
Destruction is not limited to just hard drives. All magnetic media should be shredded. This includes CDs, tapes, and disks.