Here are a few Firefox Extensions that I consider essential.
The Adblock Plus extension can strip nearly every kind of ad out of web pages, including Flash and Java applets, as well as help prevent pop-ups.
The Bookmark Sync and Sort extension imports/exports XBEL-formatted bookmarks and can synchronize a bookmarks file across multiple installations by uploading to an FTP or WebDAV server, as well as sort all local bookmarks.
The Copy Plain Text extension allows you to Copy text without formatting. This can be useful when pasting into other applications (such as OpenOffice or Word) that support formatted text.
The Download Statusbar extension allows you to keep track of ongoing and completed downloads in a hide-away statusbar.
DownThemAll makes it easy to download all links or images on a page in one shot.
EZNav allows you to middle-click on the navigation buttons for different effects. Forward and Backward increments or decrements numbered URLs, and reload navigates up in the URL hierarchy.
Favicon Picker 2 adds a new option in the Bookmark Manager to allow you to manually select (or clear) the Favicon associated with each bookmark.
ForecastFox displays current and forecasted weather in your status bar.
The Greasemonkey extension allows users to add custom scripts to change the behavior of any web page. Many pre-written scripts can be found at Userscripts.org.