An increasing problem is the fact that most new "classified documents" are electronic. These take up less physical space than paper documents, but are also easier to pilfer. Another problem, an old one that's gotten worse since the war on terror began, is the habit of classifying stuff that doesn't have to be secret. The attitude seems to be, "better safe than unclassified," so the amount of classified data is growing even faster than the cost of taking care of it.
The cost of maintaining state secrets in the United States went up at least ten percent last year. It currently costs over $10 billion a year to maintain classified information. This is the total cost for government (including the CIA, whose cost data is itself classified) and industry. The majority of the costs are for doing background investigations for people getting security clearances, or getting those getting them renewed, and for physically housing and safeguarding classified information. Over a billion dollars a year goes to the background investigations, the smallest portion goes to actually classifying a document (a little paperwork), but most of the money goes to storing the secrets in a secure fashion.