PeoplePods is an open source toolkit built with PHP/MySQL for creating websites with social networking capabilities with ease.
It can be used to build stand-alone sites or layered onto existing sites for adding social functionality.

It has the popular social functionality such as:
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friend lists
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personalized content views
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bookmarking
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voting, etc.
and standard web application features like:
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log-in
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personalization
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content creation and management
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& more
The toolkit is object-oriented & comes in 3 pieces: the core, plugin modules & administrative tools.
PeoplePods has support for theming & can be improved further easily with its plugins module.
Requirements: PHP, MySQL
jParse is a jQuery plugin for parsing XML that was fetched with the jQuery .ajax method.
It can select the value of any XML node or a node's parameter & can ouput a totally customized HTML.

The plugin is very flexible & offers features like:
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running callback functions before it starts & after it finishes
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limitting the number of <items> to be processed
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excluding XML nodes with certain words, numbers or symbols
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output the number of <item>'s in a feed anywhere in your document
As jQuery .ajax method does not allow cross domain Ajax requests, the XML must be on the same domain.
To see how easy it is to parse a XML file with jParse, check the demo.
Requirements: jQuery
Compatibility: All Major Browsers
TableGear is a MooTools plugin for adding extra functionality to the standard tables.
It is designed to work in a PHP/MySQL environment & can be implemented very quickly.

TableGear makes the following possible:
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sorting & pagination of data
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onClick editing of columns (ajaxed)
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adding/deleting rows (ajaxed)
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styling columns
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& more
The plugin is keyboard-friendly for a faster navigation & it is very well-documented with lots of examples.
Requirements: MooTools 1.2.1+ & PHP
Compatibility: All Major Browsers
AJAX Upload is a free script for easily impelementing Ajaxed upload interfaces.
It comes with ready-to-use server-side code for PHP, ASP.NET & Coldfusion.

The script doesn't require any JS library to run & compatible with any of them (the example code uses jQuery).
As the upload function is fired with JavaScript, it is possible to use any object/image as the upload button which makes stying much easier.
AJAX Upload provides access to every level of the upload process (before, after, onComplete) for a better customization.
Requirements: PHP, ASP.NET or Coldfusion
Compatibility: All Major Browsers
slideViewerPro is a totally customizable jQuery image gallery plugin.
It is derived from the popular slideViewer plugin & offering more features.

The gallery is created from an unordered list with any number of images.
Some of the features are:
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display images automatically
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show captions on/off
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shuffle on/off
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custom prev-next buttons
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ability to define the animation & slide periods
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& more
The look & feel can be customized via CSS and from the settings of the plugin like the borders, colors, etc.
Requirements: jQuery
Compatibility: All Major Browsers
Notimoo is a lightweight MooTools plugin (4kb) for displaying growl-like notifications.
It comes with several options for a better customization of "how the plugin functions".

Some of the options are:
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if it should disappear automatically or not
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time it will be displayed for
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position of the notification
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display a title or not
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opactiy of the modal window.
It is also possible to update the look & feel of the notifications via CSS.
Requirements: MooTools
Compatibility: All Major Browsers
Chroma-Hash is a jQuery plugin that aims to offer a better password input experience.
The Problem:
A standard password field replaces the entered characters with "●" characters. The problem is "we never know if we made a typo or not until the form is submitted & a reply is received from the server".

The Solution:
Chroma-Hash, "converts the values entered" into a colored visualization.
A user filling the password field can easily recognize that if the colors are the usual equivalents of the password or not. And, anyone who sees the colors won't have any idea what the actual password is.
The script can also be used to visualize password confirmations (password & confirm password fields).
P.S. A detailed info on the method & security concerns can be found at the developer's related post.
Requirements: jQuery
Compatibility: All Major Browsers
Thematic maps are very useful when describing statistical data about places. The data, simply, becomes much easier to understand.
Cartographer is a JavaScript library for creating thematic maps on Google Maps which supports custom styling.
It is only a one JavaScript file that relies on the powerful Raphael.js vector-graphics library.

It supports 3 visualizing types:
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Chloropleth (color coded regions)
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Pie charts
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Point clusters
The areas on maps are mentioned as latitudes or regions (depending on the type) which means no hacking or manual calculations.
Every visualization type comes with different options like colors, opacity, stroke & more.
P.S. The library is currently on alpha state but pretty solid.
Requirements: RaphaelJS JavaScript Library
Compatibility: All Major Browsers
The Fluid Grid System is a CSS framework which combines the principals of the typographic & baseline grid into a resolution-independent one.
It has a comprehensive logic. The classes are mentioned like: six_column section or three column which makes it easier to use & understand.

With the simple layout & use of CSS, the Fluid Grid System degrades well in both older web browsers, scales with text nicely & presents content to screen readers in a logical manner as well.
The framework is also great for rapid prototyping besides final production layouts as designers can quickly design complex layouts.
Compatibility: All Major Browsers
Script.aculo.us is the most widely used add-on for the Prototype JavaScript Framework with the features like animations, drag'n drop, Ajax control & more.
Its second version, renamed as Scripty2, is out with a complete rewrite. It is lightweight (5kb compressed), flexible & works faster.

The library is currently in alpha status & there are still parts that need to be developed or improved. On the other hand, it is very promising & already being used by several big projects.
And, besides the Scripty2 homepage itself, the demos show how it will be empowering Prototype JS.
Requirements: Prototype JS
Compatibility: All Major Browsers