There are two kinds of paper that will flow across your desk (or through your computer): the official Cornell stuff that needs to get taken care of in a timely fashion and the unsolicited mail that comes generically from the outside to the "Chair of Department X."

Official stuff

Some times of the year are busier for chairs than other. The busiest time is often in spring when various end-of-the-year activities need to be planned.

Unsolicited mail

Chairs get a ton of mail. Anything addressed to the department rather than to an individual will come to you. You can ask a support staff member to do an initial sort of your mail, putting into a separate box items that are clearly not time-dependent (book catalogs, program announcements, etc.). Going through this box only once every week or two will save you a bit of time.

Much of the unsolicited mail can be tossed, but some of it will need attention, or at least filing. The latter includes unsolicited letters from individuals seeking to teach in the department. Colleges do not fill regular positions from such letters, but if the person looks at all interesting, it's good to keep the letter on file in case the department suddenly needs a temporary hire. Other potentially useful stuff includes things like brochures or flyers on graduate programs, internship opportunities, events in the region, etc. Have a system for keeping track of this kind of thing-it might be posted on a departmental bulletin board, or kept in files for the use of students and advisors.