Ten broadly useful extensions, as detailed at: http://bit.ly/10Xxc (There are technically 10, but Gears can't be installed from Mozilla's site)
Blocks annoying video ads on YouTube, Facebook ads, banners and much more.
Adblock Plus blocks all annoying ads, and supports websites by not blocking unobtrusive ads by default (configurable).
The first and only download manager/accelerator built inside Firefox!
Tab Mix Plus enhances Firefox's tab browsing capabilities. It includes such features as duplicating tabs, controlling tab focus, tab clicking options, undo closed tabs and windows, plus much more. It also includes a full-featured session manager.
Xmarks is the #1 bookmarking and open tab add-on. Keep your bookmarks, and open tabs backed up and synchronized across computers and browsers. Mobile phones with Premium access. Utilize LastPass to sync passwords!
Bring back your personal and powerful Firefox Button!
Add useful extra features to Gmail, like hierarchical labels, an unread message icon on your browser tab, file attachment icons, and more.
Select text and it's automatically copied to the clipboard. Also pastes on middle click.