Regarding Firefox, I found that if you use a master password:
Use a master password: Firefox can protect sensitive information such as saved passwords and certificates by encrypting them using a master password. If you create a master password, each time you start Firefox, it will ask you to enter the password the first time it needs to access a certificate or stored password.
Hopefully none of the downloads mentioned in this thread will reveal this master password. If they do I'd like to know.