Depending on what you actually want to do with the password, you may have to store it in plain-text. Most CHAP implementations require this, for instance. What does using CHAP get you? You’re not asking the client to send his secret over the wire. This is obviously a good thing. Other examples of security protocols that depend on both parties sharing a known secret (e.g. a password/username pair) with similar characteristics can be easily found.
For web development – in particular, for implementations of a classic web “login” service – here are some symptoms that may indicate that you probably need a plain-text password somewhere:
*) One of your requirements is to offer a “password recovery” feature
*) The secret is going to be re-used for other types of authentication (think “Single Sign-On”) that require plain-text secrets
*) The secret may need to be shared with other partners who are unwilling or unable to deal with using your authentication service