How To Configure Firefox To Always Run In Private Browsing Mode

Mozilla Firefox (3.5 onwards) has a cool feature that can allow one to surf the internet even on a shared computer and leave no trace behind (history, cookies etc). This is called Private Browsing feature and is useful when a single login id is being used to access Firefox and other applications on a computer. It can be enabled by simply hitting Ctrl + Shift + P or through Tools > Start Private...