Firefox – How to make firefox use known passwords without prompting

You should look at the add-on lastpass.

This keeps all your passwords online and encrypted so only you can access them. However, they're accessible anywhere in the world.
It has too much functionality to detail here, but is quite complete regarding features.
Available for Windows, Mac and Linux, in my experience it's the best password manager.

Keepass seems to be the best available password manager.

Info:

What is KeePass?

Today you need to remember many passwords. You need a password for the Windows network logon, your e-mail account, your homepage's FTP password, online passwords (like website member account), etc. etc. etc. The list is endless. Also, you should use different passwords for each account. Because if you use only one password everywhere and someone gets this password you have a problem... A serious problem. The thief would have access to your e-mail account, homepage, etc. Unimaginable.

KeePass is a free open source password manager, which helps you to manage your passwords in a secure way. You can put all your passwords in one database, which is locked with one master key or a key file. So you only have to remember one single master password or select the key file to unlock the whole database. The databases are encrypted using the best and most secure encryption algorithms currently known (AES and Twofish). For more information, see the features page.

How to install for the MAC:

Running KeePass under Mono (Linux, Mac OS X, BSD, ...)

In addition to Windows, KeePass 2.x runs fine under Mono, i.e. Linux, Mac OS X, BSD, etc. In order to run KeePass, follow these steps:

1. Install Mono ≥ 2.6 (older versions will not work and are not supported). Depending on your platform, the packages to install are called mono-stable, MonoFramework, mono-devel or mono-2.0-devel; see the Mono project page, if you are unsure which packages to install. On some platforms, the Windows Forms implementation (System.Windows.Forms) is offered as a separate package; KeePass requires this package, so if you see one, install it, too.
2. If you want to use auto-type on Linux / Mac OS X / BSD / etc., you additionally need the xdotool package.
3. Download the portable version of KeePass (file KeePass-2.xx.zip) and unpack it in a location of your choice.
4. When being in the KeePass directory, run the command line "mono KeePass.exe". Alternatively, right-click onto the KeePass.exe file, choose "Open with Other Application" and type in mono as custom command.

For the last step you might want to create a shortcut or shell script file with this command line (use an absolute path to KeePass.exe, if the shortcut / shell script file is in a different location).