With the myriad of online services that require password protection, password management in your Web browser has become a practically essential service. Most browsers, including Apple's Safari browser for OS X, have some form of password management built-in, and when you visit a site that requests authentication, the browser should prompt you to save the entered credentials. However, some Web sites may be specifically built so browsers will not store passwords.
This feature is great for some sites, such as banking and medical sites which contain private and sensitive information; however, there may be others that you use for more benign purposes, which still prevent Safari from saving passwords.
When you encounter one of these sites, Safari may show you a small message at the point of password entry which claims the site has requested Safari not save your password.
For these sites, Safari can still save the password, though it is not a default option. To do this, go to the Passwords section of Safari's preferences, where you will see a checkbox at the bottom of the window which says "Allow AutoFill even for websites that request passwords not be saved." Toggle this setting, and you should now be able to save your site's password.
Do keep in mind that with this setting, Safari may try to save the passwords for financial and medical services as well, so to prevent saving passwords for these sites you may have to be a little more careful when prompted. If you do inadvertently save a password, you can easily remove it by again going to the Passwords section in Safari's preferences, searching for the site, and then selecting it and clicking the Remove button.