Firefox comes loaded with shortcuts and conveniences, but many are tame and unobtrusive. As an extension, the free FastestFox add-on offers unorthodox productivity features that you won't see added to the main branch any time soon. The features are wide-ranging, and you will probably want to disable some of them, but in general they are inventive and helpful.
A characteristic feature of FastestFox is "Endless Pages." If you scroll to the bottom of a page in a series (e.g. a photo album or a chopped article), the next page is automatically downloaded and rendered below for easy scrolling. While often useful, this is annoying when unwanted, and unfortunately there are no controls to tweak its activation. Other features center on direct page manipulation: There are options to add Amazon and Twitter results to the top of Google search pages, and a "Related Articles" sidebar to Wikipedia pages. Whenever you highlight text, a set of small icons pops up which allows you to search for the text on a customizable selection of sites. FastestFox also includes qLauncher, an interface which gives hotkey access to bookmarks.
Because there is such an array of features in FastestFox, it is unlikely that you find all of them useful. I disabled the additions to Google search pages because it seems invasive (and Google is getting cluttered enough already). I got rid of the pop-up search buttons too, because I click them more accidentally than purposely. But for others, these may be key features.
FastestFox's best feature is the addition of Google search results to the AwesomeBar. As you type in terms, Google results appear right underneath the usual history results, saving you a visit to the search page. If you search frequently, this small optimization will multiply out to significant time savings. The other features' utility may depend on personal preference, but this enhancement alone makes FastestFox worthwhile.