I do not require passwords to be changed on a schedule in my application for a simple reason: it makes remembering passwords harder and is thus more likely to lead people to write them down somewhere or otherwise use an unsafe memory aid.
What arguments are there to the contrary? Why would forcing someone to change a password that no one else knows make it more secure?
Note: since this is open to opinion and debate, I'm marking it as a community wiki. It is, however, centrally a technology concern so I think it reasonable to post here.