Mods: apologies if there is already a thread about this, but I did a search & didn't see 1.
As the title says, this thread is for people to post useful extensions for Firefox.
1-ClickWeather: Instant local weather, alerts, radar in motion, satellite maps, and forecasts.
ActionShow!: Hover over a button [e.g. submit, etc] to display the button's url destination in the status bar.
Adblock Plus: Ever been annoyed by all those ads and banners on the internet that often take longer to download than everything else on the page? Install Adblock Plus now and get rid of them.
Adblock Plus: Element Hiding Helper: Fight the text ads! Element Hiding Helper is a companion extension for Adblock Plus meant to make creating element hiding rules easier.
Antipagination: Allows you to see google search results on one gigantic page. Right click "next" link and select Antipagination, All. It also works on other pages with next or previous buttons. It also works in pages encoded with different character set (language).
Bookmark This Page Plus: Adds a menu item in each sub folder of the bookmarks menu to bookmark the current page. [Just like Opera & Maxthon]
Cookie Button: A button placed in the firefox toolbar allowing one to change cookie permissions for the host of the current page. Turn cookies off in Firefox's privacy options, then use this button on a per-site basis, that way you need never worry about sites dumping cookies on your computer without you knowing about it, as you'll only get the ones you give permission for.
CustomizeGoogle: Enhance Google search results and remove ads and spam. [0.74 released
today, fixes bug(s) from 0.73]
CuteMenus2: Iconifies your menus and popups with XP skin.
DiggiDig: It allows you to navigate up the directory tree with just a few mouse-clicks.
Firefox 1.5 - 2.0.0.* [works with 3 if you tell it to ignore version checking, see MR Tech Toolkit]
DragNDrop Toolbars: Your toolbars become Drag'N Dropable!
Easy DragToGo: Allows you to open links in new tabs, search texts, save images and do more with drag and drop gestures easier.
Edit Middle 2: Show AwesomeBar results when editing in the middle (not just at the end)
Firefox 3.0pre - 3.0.*
Extension List Dumper: This extension adds a button ("Dump list") to the Add-ons window. When this button is pressed, a new window is opened with the list of installed extensions, themes or or plugins. This extension is useful to keep a list of your extensions and themes, or when reporting a bug or a conflict to an extension author.
Favicons Downloader: This can be used to update bookmarks with no favicons (they've expired, they're new, etc). To use this, look underneath the 'Tools' menu for the new entry. [it can take a while if you have loads of bookmarks, but it doesn't stop you from carrying on using Firefox while it's doing it.]
FavLoc: FavLoc allows you to set folders as "favourite locations" to which you can easily download. FavLoc menus will appear on the File menu (for saving pages), the context menu (for saving images and links), and on the download prompt.
FfVb: Gives you some extra functions when using vBulletin based forums. It handles the task of ignoring users better than the default vB ignore function, you can select specific users to highlight [it highlights their whole post, though sadly it doesn't let you pick a different colour for each person], & you can even ignore whole threads [it hides them completely]. So far I've only found 2 forums that it won't work on, 1 is the bit-tech.net forum [of the ones I've tested, they're using the oldest version of vB - 3.0 - maybe that's a problem?], & no prizes for guessing which other forum it doesn't work on... yup, CF.

At first I thought it might be because CF is running the latest [I think] version of vB [3.7.2], but then on a hunch I checked it on vB's own forum & it worked there, so...

maybe Paul M's done some tweaking behind the scenes that causes the extension not to work [either by design, or just coincidence].
File Title: With this extension you can save HTML pages like in Microsoft Internet Explorer. Default filename is generated according to HTML tag TITLE.
Filter Extensions: Adds a search box and a filter drop-down to the Addons window, to filter your installed extensions. [very useful if you have quite a few installed, like I do

]
Find All: This add-on replaces the find bar's Highlight All button with a powerful Find All button, which highlights all search terms found and displays them in an easy to view list. The list displays a few words before and after the search term so you can quickly see the context of each match. It also shows a total of how many times the search term was found on the page.
Firesomething: All your branding are belong to Firesomething. This extension will give Firefox an identity crisis by generating a new randomized browser name every time you open a new window. Confuse your friends and family with names like "Mozilla Firebadger" and "Mozilla Poweroyster". [If any mods have noticed odd browsernames in the server logs, now you know why.

]
Firefox 2.0 - 2.0.0.* [still works with 3 if you override version checking]
Handy Extra Stuff: Adds some handy extra toolbar and other functionality to Firefox, including: Popup (in a tooltip) ALT text and other attributes, Copy ALT/TITLE text, Custom webpage source viewer button + configuration dialog, Toggle online/offline button, Tabbar customization UI, Browser behavioral tweaks for developers.
HistProp: Adds a Properties item to the browser's History viewer context menu.
IdentFavIcon: IdentFavIcon is based on the idea of Don Park called identicon to generate visually pleasing and easily recognizable icons from identifiers, such as IP addresses. This extension replaces the default favicon for web pages without one with a visually pleasing identicon, which is unique for each domain. The extension uses the CRC-32 code of the web page's domain name to seed the identicon renderer.
iMacros for Firefox: Automate your web browser. Record and replay repetitious work. [I have this 1 installed, but not actually got round to trying it yet, but it looks interesting].
IMDb Preview: Preview movie & actor posters when hovering over their IMDb links. Useful if you've ever gotten fed up having to choose between squinting at the tiny pics next to cast listings or actually going to the person's page & back again when you want to put a face to a name. It also works for links posted anywhere on the net, as long as it goes to a valid IMDb movie/program or person page.
InFormEnter: Helper for form filling in semi-automatic mode.
JSView: All browsers include a "View Source" option, but none of them offer the ability to view the source code of external files. Most websites store their javascripts and style sheets in external files and then link to them within a web page's source code. Previously if you wanted to view the source code of an external javascript/stylesheet you would have to manually look through the source code to find the url and then type that into your browser. Well now there's a much easier way.
Mark Unsecured Password Elements: MUPE marks any password elements that use http submission [instead of https] or appear on http pages in red, to call attention to the fact that they are unsafe.
Firefox 3.0 - 3.1a1pre
MeasureIt: Draw out a ruler to get the pixel width and height of any elements on a webpage.
Menu Editor: Customize application menus.
Mouse Gestures Redox: Execute common commands with the mouse.
MR Tech Link Wrapper: Wraps long links to spare you from having to scroll left and right.
MR Tech Toolkit (formerly Local Install): MR Tech Toolkit power tools for all users.
NoScript: The best security you can get in a web browser! Allow active content to run only from sites you trust, and protect yourself against XSS [cross site scripting].
Open In RegEdit: Select registry keys in the page and open them in the registry editor.
Override Mozilla Firefox Guidance: Randomly implements several essentially unhelpful - yet almost funny - error pages, when a website cannot be reached. [Some pages may contain foul language and/or sound offensive to some people.]
Firefox: 3.0b5 – 3.1a2pre
Prognos: This extension will look through the links on a page and find IMDB and YouTube links. It'll add the title of the YouTube or IMDB page to the link so you know what you're clicking on. So change a link that says "watch this video!" into "watch this video (Rick Roll)" or change a link that says "this movie" into "this movie (Wall*E (2008))".
Quick Preference Button: Adds menu button for quickly accessing common preferences.
Redirect Remover: Removes Redirects from Links and Images
Firefox 3.0b1 - 3.0.*
Research Word: Quickly lookup a word or phrase simply from the Context Menu on selected text or via Address Bar shortcuts.
Resizeable Textarea: Resize textareas to your needs.
Show Go!: For those who miss having the Go button in the address bar all the time in Firefox 3.
Statusable: Statusable is a firefox extension that creates a second statusbar, reserved for the progressbar and standard statusbar text (usually used for link destinations).
Sxipper: It's 1 of those thingies for remembering your passwords etc for logging in to different sites. Quite easy to use, & quite a slick look & feel to it.
Tab Counter: A simple extension that counts the number of open tabs per window and displays the count in the toolbar.
Tab Mix Plus: A whole bunch of tab related functions, very useful. You'll need the version from the homepage I've given the link for, as it's a newer version than the 1 on the Mozilla add-ons site, & you need the newer 1 for Firefox 3.0.1.
Tab Scope: Shows a popup on tabs and enables you to preview and navigate tab contents through popup [works with the drop-down tab list at the end of the tab bar as well].
Toolbar Buttons: This Extension adds buttons to the Customize Toolbar Window.
TubeStop: Stops YouTube videos from automatically playing as soon as the page has loaded.
Undo Closed Tabs Button: Add a toolbar and/or tab bar button to undo closed tabs
Firefox 3.0b5 - 3.0.*
Update Notifier: Notifies you when updates are available for your extensions and themes.
ViewSourceWith: View page source with external application.
That's not all of the ones I have installed, just the better ones.