The Firefox tabbar is always visible in the web browser unless it is permanently deactivated in the View menu (Update: this feature has been removed from Firefox 23). It does not really make sense to deactivate it unless there is never more than one website open on the computer system.
What’s missing is an easy way of hiding the Firefox tabbar when it is not needed so that it is only displayed when you need to switch tabs. This gives you a couple of extra pixels of height for the website to display in.
That’s exactly what the experimental Firefox add-on Hide Tabbar is doing. Hide Tabbar works by configuring a keyboard shortcut to hide and display the tabbar in the web browser. The default combination has been set to CTRL F11 which is not that comfortable as it can only be accessed with both hands.
The keyboard shortcut can be changed easily in the options of the add-on so that only one hand is needed to hide and display the tabbar in Firefox. Hide Tabbar offers an auto-hide function as well which will automatically hide the Firefox tabbar after a certain time. The tabbar will be displayed again if the user hovers the mouse cursor over the area were it was initially displayed.
Hide Tabbar is an experimental add-on for the Firefox web browser that is compatible with all versions of Firefox.
Update: Please note that the extension is not working properly anymore in newer versions of the Firefox web browser according to user reviews on the add-ons page over at the Mozilla website. I suggest you do not make use of it anymore to hide the tab bar as you may lose tabs or experience other issues while it is running.
There is no comparable extension available for Firefox at the time of writing.
Update 2: Hide Tabbar has been resurrected. The add-on is once again compatible with all recent versions of the Firefox web browser. It features one new option; you may use it to reopen the tabbar automatically when a new tab is added to the browser (For instance by using Ctrl-t to do so or by middle-clicking links in the browser).