Wikipedia's current list of user scripts is in bad shape, in that it is disorganized and contains many non-working or obsolete entries. It is therefore set to be deprecated, and the list below is set to replace it.

Add scripts here that are confirmed working and relevant. Non-working scripts should be listed here.

For the sake of easy editing, scripts should be listed as *[link] - [description]. Consensus can be established for the actual display format when the list approaches completion.

If adding to the Vector compatible section, make sure scripts are confirmed working with the Vector skin.
Scripts that don't work with the Vector skin but do work with other skins belong in the Non-Vector only section.
Where possible, link to a script's documentation page rather than the actual .js page.

Note that the old list will be preserved and linked to as a more exhaustive list of existing scripts.

Vector compatible

Multifunction tools

Several different types of tools in one script.

Navigation Popups - Adds robust page previews and other tools, accessible via popups that display when rolling over links. Enable via Preferences → Gadgets → Navigation Popups
Twinkle - Easy tagging, delete nomination, user welcoming/notifications, vandalism reverts/warnings/reports, and more. Enable via Preferences → Gadgets → Twinkle

Site-wide appearance

For readers

Scripts that offer superficial site-wide changes.

ReferenceTooltips - Adds tooltips to inline citations, so you don't need to jump away from the article text for reference information. Enable through Preferences → Gadgets → ReferenceTooltips
Sharebox - Adds social networking share buttons.
Hide Vector Sidebar - Hides the left sidebar in Vector. Can access the sidebar anytime by alt-shift-a.
SidebarTranslate - Translates sidebar language links into English, adds Google Translate links. Credit to Tra (original); Manishearth, TheDJ, Voice_of_All & Equazcion (various modifications).
Google Title - Adds a link next to an article's title to search Google for that title in a new tab.
Smaller Templates - Makes maintenance templates appear smaller, both horizontally and vertically.
Subject's Age From Year - Roll over any year in an article about a dated subject and see the age of that subject that year.
mathJax - High-quality LaTeX font typesetting via MathJax.
wiktLookup - Double-click a word, and go to its definition on Wiktionary.

For editors

Scripts that offer superficial site-wide changes primarily useful to those who edit actively, or participate in discussions.

Menu Tabs Toggle - Toggle between drop down menus and tabs in Vector. Preferences → Gadgets → Enable toggling between tabs and dropdown menus in the Vector skin.
SearchNamespace - Adds a pulldown menu next to the quick search bar allowing selection of namespace to search in.
New Pages - Adds a link in the toolbox to patrol new pages.
Link Classifier - Colorize links on the page to indicate redirects, broken redirects, disambiguation pages, and XfDs.
Mark Blocked - Marks blocked users in all listings and signatures (faded and struck-out username).
Admin Rights - Highlights administrators in all listings and signatures.
6 Tabs Vector - Shows edit and history tabs for both main and talk pages while viewing either one.
Watchlist Notifier - Notification of changes to watched pages. Changes are checked on each page load, with notifications appearing at the top of the page under its title.
Duplinks - Highlights links that occur more than once in an article (separate for lead and body).
Autolink - Makes plaintext [[wikilinks]], {{transclusions}}, and URLs clickable (for instance in .js pages, diff pages, history, etc).
Dropdown To Tabs - Changes Vector's drop-down menu items into tabs (works but not pretty).
Menu To Tabs - Same as Dropdown To Tabs, but uses jQuery.
WikiTrust - Click on text in an article to get information about who added that text, and when. Uses data from the WikiTrust project.

Editing

wikEd - Provides a comprehensive set of tools, including syntax highlighting, when editing a page. Enable through Preferences → Gadgets → wikEd.
HotCat - Quick Ajax category editing. Enable through Preferences → Gadgets → HotCat.
ajaxPreview – Fast edit preview and changes without page reloading.
Bracket Match - Check matching for template and variable brackets.
AutoEd - Cleanup various problems with markup, headlines, templates, and ISBNs.
Advisor - Flags possible issues with wikitext while editing a page.
MOSNUM Dates - Cleanup dates per WP:MOSNUM.
Common Terms - Delink common terms.
Autocomplete - Offers a popup suggestions menu whenever you start typing a link or template in the main edit box.
Split Preview - Shows editing previews beside the edit box instead of above or below.

References

ProveIt GT - Popup forms to fill in references. Enable with Preferences → Gadgets → ProveIt
Ajax Preview - Adds a button to the edit form to preview the current section, with a references section included.
HarvErrors - Displays errors when using Harv templates
SnipManager - Toolbar with forms to fill in references.

Tagging

Vandalism

rollbackSum - Rollback summary. Credit to User:Ilmari Karonen (original), User:Porchcrop & User:Alex_Smotrov (fixes).
Rollback All - Revert all contributions of a user
Mass Rollback controlled - Rollback selected contributions of a user or all contribs of a user
Igloo - Anti-vandal javascript GUI

Diffs

wikEdDiff - Adds additional functionality to diff display. Part of User:Cacycle/wikEd.js. Enabled when WikEd is enabled or through Preferences → Gadgets → wikEdDiff
Diff Time - Adds time between diffs and time since each revision.
Link Intermediate Revisions - Links the "intermediate revisions" message so it can be clicked to see a history listing of those revisions.

Discussions

Vote Symbols - Adds graphical icons to users' !votes in discussions.
Comment Highlighter - Highlights your discussion comments.

User pages

User Info - Shows edit count and time registered.
Sysop Detector - Shows user rights groups. Credit to User:Splarka, fixed by User:Equazcion.
ContribsTabVector - Adds contribs and stats tabs to user and user talk pages.

Listings

Watchlist

Smart Watchlist - Watchlist customization and organization.
Watchlist Links - Adds some useful links to your Watchlist.
Catwatch - Shows the addition of pages to specified categories on your watchlist.

Recent Changes

What links here

History

Active Watchers - Adds a link to History pages, next to the "Number of watchers" link, to show the number of active users watching the page ("active" defined as users who have logged in within the last 30 days).
Live Diff Link - Show a live-updated diff link at the top of History pages while you select revisions, so you don't need to actually load the diff to get a diff link.

Logs

New Page Patroller - Adds another box to the sidebar that shows a regularly updated list of new pages

Contributions

Hide Top Contribs - Does the opposite of the "Only show edits that are latest revisions" checkbox. (There is also an it.wikipedia.org-specific version, which has some "special" problems with some skins, but it still displays somewhere!)

Administrative

DYK Check - Tool for checking Did You Know eligibility.

Miscellaneous

Prose Size - Adds the page size of the article to the toolbox

Meta-scripts

Non-Vector only

Editing

Format Citations - adds one tab to harmonize whitespace in citation templates, and another to convert them to the vertical format. Only tested in the modern skin.

Discussions

Edit Count - Adds a quick link in the toolbar for checking one's edit count. (Especially for those who have editcountitis!)
Contribs Tab - Adds a contributions tab on user and user talk pages.

Vandalism

RC Patroller - Adds a porlet to the sidebar that shows a regularly updated list of recent changes