Here are what I would call the ESSENTIAL Add-ons. If I don't have these I don't like Firefox. A few are luxuries though, like fire.fm but they don't slow it down so they can stay :)
The simplest YouTube Video Downloader for all YouTube Flash sites, period.
Download all the links, movies and audio clips of a page at the maximum speed with a single click, using the most popular, lightweight and reliable external download managers.
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!
A customizable mouse gestures extension which enables to execute various commands and user scripts with six types of gestures.
The original Gmail notifier for multiple accounts. Allows you to receive new mail notifications along with viewing account details including unread messages, saved drafts, spam messages, labels with new mail, space used, and new mail snippets.
View and manage downloads from a tidy statusbar - without the download window getting in the way of your web browsing.
Thanks Tekzilla for your awesome review! Click here to see their video: http://youtu.be/BUDqWrJ-Vao
Shows the URLs of all the tabs in a textarea so that it can be copied easily.
This extension adds desktop shortcut creation to the context-menu for Windows, Linux and Mac.
Organize your search engines with separators and folders.
Note from Mozilla: This add-on has been discontinued. Try DragIt instead.
Allows you to open links in new tabs, and do more with drag and drop gestures easier.