Use The Force: Save Your Password
I can't name the exact date, but at some point Gmail stopped allowing you to save your password. You see, web browsers (like Firefox, Internet Explorer, etc) obey rules set in HTML code, and Gmail is one site that uses the code autocomplete="off" in their password field in their login form - forcing the browser to not store and fill in your password for you.
Now I know that Gmail offers to remember who you are, but I don't like that option. Plus if you are accessing several accounts from the same computer that option is no good.
Firefox Extensions to the rescue!
Eric at roachfiend.com (who writes FF extensions as a hobby) has written an excellent extension call Always Remember Password and it forces Firefox to ignore code telling it to not remember passwords.
Firefox still asks you if you want to remember a password on a form or not, you don't lose any control.
It's simple and great. Once installed you don't have to do anything, it works accross all sites (not just Gmail).