Firefox allows users to extend or completely alter existing functionality using extensions (typically small packages/applications). Rather than requiring someone to edit the source, these changes can be loaded like a plug-in, easily disabled or uninstalled. Extensions can be as simple as adding a single menu item or as complicated as completely changing the application interface.

Combo Tab Icons v0.1.4.7 (Firefox 2.0-3.5.*; screenshot):
Combines the site and close tab icons. The site icon is only visible when the tab is busy, displaying the throbber.
Note: No plans to update for 3.6+. Will likely need more than a maxVersion bump.
Data Sync v0.1.8.5 (Firefox 3.0-4.0.*; screenshot):
Synchronize selected profile data to a remote server (of your choosing). Think a simpler version of Google Browser Sync or Mozilla Weave, with easy extensibility.
Important: This extension can not be run out of the box. It requires an application on the remote server to handle the POSTing of XML data. A PHP example is included. Carefully read the documentation as there are inherent privacy issues with this extension.
  * Use your own server: You decide where to store the data. All you need is a web server and an application to process the transactions (see example server.php).
  * Data encryption: Mozilla's secret decoder ring or passphrase-based RC4 encryption methods can be selected.
  * Modular: Additional .jsm modules can be created to perform new or custom import/export functions (see sample.jsm).
  * Simple and safe framework: All you need are import() & export() functions and the extension takes care of the rest, including data transfer and encryption.
  * Automatic updates: New data can be automatically imported without any prompts.
  * Builtin modules: bookmarks, cookies, permissions, and Stylish.
Focus Last Selected Tab v0.9.6.2 (Firefox 2.0-4.0.*):
Focus the last selected tab when closing.
Similar to Gorgias' extension (of the same name), but contains only the core functionality and uses a more simplistic and reliable method to determine the last selected tab.
Open Tab Right v0.3.3.7 (Firefox 1.5-4.0.*):
Open tabs to the right.
Note: Partially deprecated by bug 465673 for Firefox 3.6, slightly different behavior.
Permission Manager v0.1.1.4 (Firefox 0.9-3.5.*; screenshot):
Adjusts the content policy settings (allowing image, cookie, script, and related objects) via the Tools menu.
Note: No plans to update for 3.6+. A maxVersion bump should suffice.
Plugin Manager v0.9.3 (Firefox 3.0-5.0.*; screenshot):
Manage plug-ins via the Tools menu.
I decided to resurrect this extension after a few recent security problems with Flash. I also wrote up a pluginManager_mb.uc.js ucjs snippet that allows you to put a selected plugin right on the Firefox' menubar for quick and easy access.
Note: Version 0.9+ uses Firefox' builtin plugin management features and now works on all systems!
  * 0.9+ has the ability to reset the state of a plugin after a specified time.
Popup Blocker Settings v0.2.1.6 (Firefox 0.9-4.0.*; screenshot):
Quickly toggle between three different modes of popup-blocking - Open all, Block unrequested, and Block all.
Adjusts dom.disable_open_during_load, dom.popup_allowed_events, and privacy.popups.disable_from_plugins.
Restore Scroll Position v0.5.9.11 (Firefox 2.0-3.1.*):
Restore Scroll Position v0.4 - old stable release (Firefox 0.9-2.0.0.*):
Restore scroll position for pages with no-cache and related headers. (see bug 215405)
Note: No plans to update for 3.5+. Deprecated by bug 215405.
  * 0.5+ can restore text inputs if restorescrollposition.formData is true (default: false).
  * 0.5.9+ uses a history event listener for better integration and more reliable operation (mouse nav should work).
  * has gone back to using the 'load' event and will no longer process page loads from Gecko's bfcache.
  * removes the .reload pref (unused since, but will continue to restore on reload.