It's worth considering that there are different types of passwords, and these have different types of security considerations.
There are personal passwords, which should be known only to one person, such as the password to your user account. There's no point in changing these often: if someone is shoulder-browsing or logging keystrokes, it's not going to matter if the password is three years old or three days old. Regular changes might actually serve to lessen the security by having people use less secure passwords or writing them down. Frequent demands for password-changes also makes some forms of phising and social engineering attacks easier.
Then there are passwords that need to be shared among a group -- the system administrator password on a large network, the BIOS password used on the company's laptops, the password to the support account on a supplier's web-page. These passwords need to change frequently, since it's hard to always perfectly manage and control who is given the password, and because people moves from the "need to know" group to the "don't need to know" group (and sometimes into the "really, really shouldn't know" group.)
Then there are passwords which are used by computer systems. They're a bit like the mad cousin nobody likes to talk about. For systems to work and do anything useful, they often need to access to other systems -- databases, back-end systems, file-servers, third-party services, the works -- and often the only practical way is to put the required passwords into the system's configuration files. If you're lucky, they'll be obfuscated, but nine times out of the they're stored in plaintext (and obfuscation isn't hard security either). As managing configurations of multiple systems quickly turn into a non-trivial task, you end up with passwords that are potential known to many people: everyone's who's responsible for the given system, system-administrators of the computers the system run on, backup administrators, anyone with physical access to the computer, anyone with physical access to the backup media, anyone with physical access to the old storage media -- and that's assuming the security system works properly, which they rarely do 100%. (For one thing, once there are problems with getting a system to work, configuration files tend to fly back and forth in e-mails.) Further, once a password is put into a configuration file anywhere, it becomes a right bitch to change, since it means changing all the places it is used. So people don't change them.