Auto Copy:
https://addons.mozilla.org/en-US/firefox/addon/383/ : Select text and it's automatically copied to the clipboard. No more need to right click and select 'copy'. When using a mouse, the middle button (or pressing the scroll) works to 'paste' the copied text.
DownloadHelper:
https://addons.mozilla.org/en-US/firefox/addon/3006/ : The best downloader I've found for sites like YouTube and many others.
DownThemAll!:
https://addons.mozilla.org/en-US/firefox/addon/201/ : The first and only download manager/accelerator built inside Firefox.
dragdropupload:
https://addons.mozilla.org/en-US/firefox/addon/2190/ : A truly heaven sent add-on for uploaders! Simply drag multiple files from your computer into the upload box at the same time, saving yourself so much time.
Image Zoom:
https://addons.mozilla.org/en-US/firefox/addon/139/ : Adds zoom and rotation functionality for images. If you have a mouse, holding down the left button and using the scroll wheel you can zoom in and out on any image.
Linkification:
https://addons.mozilla.org/en-US/firefox/addon/190/ : Converts text links into genuine, clickable links.
QuickDrag:
https://addons.mozilla.org/en-US/firefox/addon/6912/ : Extends the function of the drag-and-drop mouse gesture so that it can be used to load URLs, do a web search of selected text on a page, or save an image on a page. All with a simple drag!
repagination:
https://addons.mozilla.org/en-US/firefox/addon/2099/ : See more search results etc. on one page, connecting several pages together. This link claims it doesn't work in the newest veriosn of Firefox, but I have it and it is working, so...
Screengrab!:
https://addons.mozilla.org/en-US/firefox/addon/1146/ : Screengrab! saves webpages as images. It will capture what you can see in the window, the entire page, just a selection, a particular frame... basically it saves webpages as images - either to a file, or to the clipboard.
Text Link:
https://addons.mozilla.org/en-US/firefox/addon/1939/ : Allows URI texts written in webpages to be loaded by double clicks.