Firefox will remember passwords by default. You may have disabled this feature, or told Firefox to never remember passwords for a particular site. For Example here Gmail is not giving a save Password Option.
Steps To Follow
- Select the Security panel.
- If it isn't already check marked, check Remember passwords for sites.
- To the right of Remember passwords for sites, click the Exceptions.button .
- Make sure that the site you're trying to log in to isn't in the list.
- If it is, select the entry and click Remove.
- Click Close.
- Click OK to close the Options window
- Now that you've configured Firefox to remember passwords, try logging in to the site again.