Where possible, don't write code to handle passwords. In particular, if the application is local, try to depend on the normal login authentication by a user. If the application is a CGI script, try to depend on the web server to provide the protection as much as possible - but see below about handling authentication in a web server. If the application is over a network, avoid sending the password as cleartext (where possible) since it can be easily captured by network sniffers and reused later. ``Encrypting'' a password using some key fixed in the algorithm or using some sort of shrouding algorithm is essentially the same as sending the password as cleartext.
For networks, consider at least using digest passwords. Digest passwords are passwords developed from hashes; typically the server will send the client some data (e.g., date, time, name of server), the client combines this data with the user password, the client hashes this value (termed the ``digest pasword'') and replies just the hashed result to the server; the server verifies this hash value. This works, because the password is never actually sent in any form; the password is just used to derive the hash value. Digest passwords aren't considered ``encryption'' in the usual sense and are usually accepted even in countries with laws constraining encryption for confidentiality. Digest passwords are vulnerable to active attack threats but protect against passive network sniffers. One weakness is that, for digest passwords to work, the server must have all the unhashed passwords, making the server a very tempting target for attack.
If your application permits users to set their passwords, check the passwords and permit only ``good'' passwords (e.g., not in a dictionary, having certain minimal length, etc.). You may want to look at information such as http://consult.cern.ch/writeup/security/security_3.html on how to choose a good password. You should use PAM if you can, because it supports pluggable password checkers.