Update November 29, 2017 Firefox has changed a lot since 2009 making my list of addons obsolete. For more current information, please visit Replace Dead Firefox Add-Ons With These WebExtensions.
All-in-One Sidebar lets you switch between bookmarks, add-ons andmore in the sidebar panel.
Cookie Monster is a great add-on that provides proactive cookie management on a site or domain level basis. Via the status bar, it provides easy access to enhanced cookie functionality.
Copy as HTML Link is great when blogging, it copies the selected text as a link, into the clipboard..
Download Statusbar lets you view and manage downloads from a statusbar, without an annoying download window.
Flashblock is terrific, it blocks Flash animations unless you either whitelist the site or click on the animation. An excellent add-on that makes sites load faster since Flash is blocked.
OpenBook improves Firefox Add Bookmark dialog.
Open Image In New Tab adds more functionality to the right click menu.
Options Menu gives easier access to options for add-ons by adding them to Firefox Tools menu.
PDF Download gives you the option to view the PDF-file in your PDF-viewer or to download the file.
QuickRestart is handy when you need to restart Firefox after enabling or disabling an extension.
Screengrab captures what you can see in the window, the entire page, just a selection or a particular frame as images – either to a file, or to the clipboard.
I also use the StumbleUpon toolbar.
Tab Mix Plus adds more features to Firefox tabs.