In a perfect world where everyone has a photographic memory, we would change all of our passwords ever 30 days and be better for it. In the real world, people are often tasked with remembering the passwords for dozens of accounts with different password policies, different change policies, and differing security needs. This causes frequent forgotten passwords (leading to overuse of password recovery tools, easy to guess passwords, and password reuse.
In theory, you could simply use good mnemonic devices for passwords (see XKCD example), but in practice this is often thwarted by differing password policies. One requires special characters, the other prohibits. One has a maximum of 10 characters, the other 100. One requires caps, the other isn't case sensitive. As a result of these passwords, I've often ended up in "vicious cycles" for infrequently used accounts. I can't remember my password because I only log in every few months, so I have to reset the password. I can't remember the password the next time because I'm always having to reset it.
Bottom line: we need something better. The current state of passwords can be bewildering for a techie, and fatal to technology use for the non-technically inclined. With the proliferation of the cloud and other online services, It's gotten to the point that every single time I try to help my mom or other layperson with something on the computer, it's nothing but a battle of trying to remember to passwords.
An inclined plane is a slope up. -- Willard Espy, "An Almanac of Words at Play"