So here's a list of (what I think are) some useful FF extensions:
NoScript -- Allows you to block JavaScript, Java, etc., and only allows it for trusted sites of your choosing. Although this can be a little annoying at first, once you get used to it, it's great if you're big on added security.
Adblock -- Use this extension to block advertisements and many "hidden" things on websites, all of which could compromise security or just plain annoy you.
DownThemAll! -- DownThemAll lets you filter and download multiple links and objects within a website, all at once. So if you want to download several images, and don't feel like doing each one individually, use this extension and you'll download them all at thr same time! This is great if you do a lot of downloading.
Customize Google -- This enhances Google search results by adding extra information (like links to Yahoo, Ask Jeeves, MSN etc) and removing unwanted information (like ads and spam). All features are optional and easily configured from the options menu. This is a great feature. Not only is it nice to be able to remove spam and ads, but the enhancements made to Google are well worth it. It's one of the very first extensions I add.
All-in-One Gestures -- This extension allows you to execute common commands using mouse gestures, rocker navigation, scroll wheel navigation and page scrolling. For me, it's an absolute MUST! I couldn't function in FF without it!
Tab Mix Plus -- Tab Mix Plus enhances Firefox's tab browsing capabilities. It includes such features as duplicating tabs, controlling tab focus, tab clicking options, undo closed tabs and windows, plus much more. It also includes a full-featured session manager with crash recovery that can save and restore combinations of opened tabs and windows.
ChatZilla -- The best IRC program in my opinion. Far better than mIRC, and yes, I've used both. I've even used a third program called ViRC. Out of all three, I still prefer ChatZilla. It's simple, streamlined, and very easy to use. Even better, it's completely free with no annoying messages asking for money.
PDF Download -- Allows to choose if you want to view a PDF file inside the browser (as PDF or HTML), if you want to view it outside Firefox with your default or custom PDF reader, or if you want to download it. A very nice feature for those who get annoyed easily at PDF files.
Nuke Anything Enhanced -- Allows you to "hide" nearly any object on a website, so whatever is annoying you is gone from view! This is also handy for printing and you don't feel like wasting ink on unnecessary imagery.
BBCode -- Adds BBCode/HTML/XHTML formating to the context menu for forums. This can save you a lot of time. I use it a lot on forums. Since most forums (including this one) have input devices for bold, italics, underline, URLs, etc., it may not be absolutely necessary, but it just makes things easier in my opinion.
Cookie Culler -- An extended cookie manager (protect/unprotect selected cookies). This is the best cookie manager I've found and the easier to use, in my opinion.
FireFTP -- A real easy-to-use FTP program that works from within Firefox. I use it all the time, despite having more powerful programs such as Adobe GoLive! and Macromedia Dreamweaver (both of which have FTP programs built in).
Image Zoom -- This does just what it says. It allows you to "zoom in" and "zoom out" on an image. It's useful.
Add Bookmark Here -- Allows you to add bookmarks to any folder in the bookmarks menu like in Opera. At first glance, this may seem unnecessary, but it allows you to add bookmarks outside of the folders. It's really a nice option.
ShowIP -- Shows the IP address of the current page in the status bar. It also allows querying custom services by IP (right mouse button) and Hostname (left mouse button), like whois, netcraft. Additionally you can copy the IP address to the clipboard. It'll also tell you your IP address as well.
TinyURL Creator -- Basically, this turns extremely long URLs into very short URLs, which makes managing them a lot easier. It also makes sending the URLs to people (or posting them) a simpler proposition.
HTML Validator -- This adds HTML validation to Firefox. It shows errors and warnings in the form of an icon in the status bar while browsing. It'll also bring up the source code for you and show you exactly what needs to be fixed. This is a nice little feature if you're doing a lot of website creation.