Best Firefox Extensions

This is an attempt to list the best extensions for the Mozilla Firefox web browser. Extensions are mostly available from addons.mozilla.org, with more available at mozdev.org and extensionsmirror.nl. See also Firefox Tips & Tweaks.

Killer

AdBlock makes a huge difference after only minimal set up.
All-in-One Gestures provides a heap of useful gestures.
Download Statusbar / Nightcap instead of a window, tidily shows downloads in a bar just above the status bar. Be sure to read my Download Statusbar use/customisation tips.

Super DragAndGo drag any text to go to that URL or google that text; drag an image to save it.
FastDic / DictionarySearch / Dict high-speed dictionary lookup (you can add Acronym Finder, etc.)
Text Link / Linkification convert plain text URLs into clickable links.
Resizeable Form Fields / Resizeable Textarea easily resize any textarea, select, etc.
Sage an RSS reader.
BugMeNot provides logins to free-register sites like NYTimes.
Gmail Notifier / Gmail Manager new mail count in the status bar, one-click access to your inbox.
Tabbrowser Preferences in particular, the option to not wipe out your current tabs when you open grouped bookmarks (thanks, Mozilla!)

Web Developer dynamic CSS editing, resize to 8x6 and ctrl-shift-H to validate is only the beginning.
FireBug great debugger for Javascript, Ajax, etc.
IEview / IE Tab opens pages in IE, great for quickly checking how badly IE has munged up your page.
HTMLtidy Validator handy validator program, integrates with View Source.
LinkChecker elegantly checks and colour-codes all links on a page.

Copy URL + gets the page title, URL and quotation all at once. Can also be customised.
Paste and Go go straight to a URL from the clipboard.
Nuke Anything / Nuke Anything Enhanced feel the power.
FlashBlock replaces flash objects with an 'activate' button.
CustomizeGoogle number search results, remove ads, rewrite image URLs directly to the image, etc.
Linky open all selected links in tabs, open all linked images in tabs, etc.
Menu Editor allows full customisation of the right-click context menu.
lget / Get File directly download (rather than open) a URL.

TargetAlert / Link Alert / smart-cursor puts an icon next to links that open PDFs, Word, mailto, new windows etc.
GooglePreview shows a thumb-shot page preview by each google result.
FoxyTunes allows control of winamp (and many others) from within Firefox.
down Them all / Magpie bulk saving images, etc.
FlashGot allows downloads to be diverted to your manager of choice.
Bandwidth Tester because we like to know these things.
Greasemonkey lets you to add "user scripts" to any webpage to change its behaviour (cf. Platypus.)
Forecastfox / Forecastfox Enhanced popular weather extension.
ChatZilla a lightweight IRC client.
Mozilla Calendar a calendar.
PDF Download choose to view a PDF file inside the browser (as PDF or HTML) or download it.
NoScript allows JavaScript execution only for trusted domains of your choice.
StumbleUpon one of those social bookmarking type things.
Firefox Showcase / Viamatic foXpose / Reveal funky feature derived from Apple's Exposé.

Google Browser Sync continuously synchronizes your browser settings (bookmarks, history, cookies, passwords) and restores your session tabs/windows across your computers.
dragdropupload drop files into attachment boxes instead of browsing for them - or even directly onto Gmail's "add attachment".
VideoDownloader Download videos from Youtube, Google, Metacafe, iFilm...
How'd I Get Here remembers how you first discovered a site.
Tab History new tabs retain the session history of the parent tab.
Aging Tabs best feature: you can actually see which tab you're on!
Tab Effect switching tab is animated like OS X switch user. I don't have this installed, but it was certainly cool to see once.
AddArt like AdBlock, but intead of blank space you get contemporary art.
ThumbStrips see thumbnails of your history in a filmstrip format. I love the concept but didn't get any real use out of it.

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This list was compiled by db with contributions from others in this forum thread. Feedback or suggestions via either of these channels is welcome.