Many employers who post jobs in newspapers or on the web have a "drop dead date" by which time applications are due. Unfortunately this is usually followed by a version of "don't call us, we'll call you." Waiting and hoping for "the call" can be very stressful.
While I understand that responding to the 100's if not 1,000's of possible applicants is not feasible, one solution would be to let applicants "off the hook" so to speak by also posting a "final notification date." In effect, if you haven't been notified by this date - preferably 4 weeks or so after the drop dead date, then you have not made the infamous short list and should put this opportunity behind you.