Must-Have UI-Fixing Firefox Extensions
Although full-fledged tab-browsing is the functionality that's most lacking in Firefox 1.0, there are other lesser areas that could also use more polish. These extensions fix user-interface (UI) glitches.

DeskCut by Evan Eveland
Lets you right-click anywhere on an open Web page and choose Create deskCut from the pop-up menu to place a Firefox bookmark on your desktop.

Resize Search Box by Nathar Leichoz, Awan Afuqya
Creates a drag-and-drop resizable version of the Google (or other search engine) search box on your Firefox toolbar.

IE View by Paul Roub
IE View adds a context-menu item that lets you open in Internet Explorer any Web page currently displayed in Firefox.

FirefoxView by Alex Sirota
This unique Firefox extension is sort of the reverse of IE View. It installs in Firefox, and from there, offers the ability to install and uninstall a modification to Internet Explorer that lets you right-click any open Web page in IE and choose the option "View this Page in Firefox."

UserAgent Switcher by Chris Pederick
The Opera browser has a nice feature that allows it to identify itself to Web servers as a browser other than Opera. Some Web sites will only display properly to Internet Explorer. UserAgent Switcher adds the same functionality to Firefox.

Stop-or-Reload Button by Caio Chassot
Combines the Stop and Reload buttons into a single button/read-out that smartly shows the functionality that's available at any given time (like Apple's Surfari browser).

Ext2Abc by Eric Hamiter
Alphabetically sorts the list of extensions shown in the Extension manager window.

Word Count by Eric Hamiter
While it might only have strong interest for writers and editors, Word Count emulates Microsoft Word's Word Count feature for use with Web-based content and does its job well. It counts the number of words in a highlighted body of text displayed in Firefox.

ChromEdit by Chris Neale
Adds the "Edit User Files" menu item to Firefox's Tools menu. When you open the program, it provides access to the four files Firefox provides for user customizations - user.js, prefs.js, userChrome.css, and userContent.jss.

Must-Have Firefox-Extension Applets
Not every Firefox extension is aimed at fixing something or adding a simple functionality. Some add little programs that do things like play music, create blog posts, or provide FTP client features. Of these sorts of extensions, here are two that I find invaluable.

Sage RSS/Atom Reader by Peter Andrews
Very nice lightweight RSS Reader that I find myself using more and more.

ForecastFox (was WeatherFox) by Richard Klein, Jon Stritar
ForecastFox is a weather display program powered by Weather.com. It displays current and forecast temperatures at a glance in the Firefox status bar. It's highly configurable and gives you quick access to detailed weather information localized to your zip code.

Tried 'Em, Like 'Em
Disable Targets For Downloads by Ben Basson
DragToTab by Nathar Leichoz, Awan Afuqya
FireFTP by Mime Cuvalo
FoxyTunes by Alex Sirota
Googlebar by The Googlebar Team
Image Zoom by Jason Adams
Linkification by John Hansen
Copy Plain Text by Jeremy Gillick
McSearchPreview by Carlo Zottmann
Nuke Anything by Ted Mielczarek
Web Developer by Chris Pederick
Tweak Network Settings by Edwin Martin
Add Bookmark Here by Mark Lindkvist

Some Extensions On My To-Try List
Always Remember Password by Eric Hamiter
BugMeNot by Eric Hamiter
Foxylicious by Dietrich Ayala
Linky by Henrik Gamal
SyncMarks by Jason Heddings
JustBlogIt by Dylan Parker
Gmail Notifier by Doron Rosenberg
TinyURLCreator by Jeremy Gillick

Tried 'Em, Do Not Like 'Em
Tab Browser Extension by Shimoda Hiroshi
Tabbrowser Preferences by Bradley Chapman

The big argument going on in many Firefox circles is: Which tab-browsing extension is better, Tab Browser Extension or Tabbrowser Preferences? A third answer is the right one: Neither. I like a lot of things about Tab Browser Extension (also known as TBE and Tabbrowser Extensions). It's a very rich program with gobs of interesting functionality, but it also has serious issues. It's buggy. The functionality is not well labeled or explained so it's very hard to control (in other words, it's confusing). And it's so large and ambitious that, according to Mozilla.org, it takes liberties with your Firefox installation. Even TBE's author appears to agree with that last statement. I prefer the single-purpose UI-fixing tab-oriented extensions like SessionSaver, Tab Clicking Options, and miniT.

Tabbrowser Preferences has the opposite problem. It offers few useful features that can't be gained from publicly-available Mozilla.org customizations. For older versions of Firefox, Tabbrowser Preferences may have offered more oomph, but for Firefox 1.0, there's not much there, there.