Vague question, elaborate please... If you are talking about storing password in browser's local memory, you can use cookies (not recommended). Alternatively you can store password for the current session in server side session ($_SESSION, in php). But if you are talking about browser's native capability to remember password for later use, there is nothing you can do in php, its a browser dependent feature. If a browser supports storing password (like firefox or IE etc), which most of the browsers do, it will automatically prompt users whether they want browser to remember this password/username.
I think the question is about, example a Remember Me option, if so all I could find at the moment is this http://www.evolt.org/node/60265 note where in the code it talks about adding a time() so cookies don't expire.
I am not sure but may be this will help you. http://www.sencha.com/forum/showthread.php?60807-Remember-password-in-browser
Do you remember Remember me check box while you logged into DP? I guess he is talking about such facility. OP you can store cookie on the client side and read it back to achieve this target.
I thought he was referring to the "Firefox remember this password?" not HTML forms. Maybe you can clarify for us OP?