It tends to be central agency departments, or departments that are in the news from time to time and that have big files--for example, Health Canada when the issue was around wait times or the Canada Health Act, or bovine growth hormone or whatever. It depends; if there's a live issue at the time, that department will tend to close up and become more strict about having things formulated through the Access to Information Act.
On October 2nd, 2006. See this statement in context.