Timeago is a jQuery plugin which enables you to display fuzzy timestamps. And, the timestamps are auto-updated.
Some example timestamps are "5 minutes ago, about 2 days ago".
Using Timeago is very functional for displaying more friendly timestamps and auto-update feature makes it more accurate when a page is opened for a while.
P.S. John Resig also has a similar solution named JavaScript Pretty Date.
Requirements: jQuery
Compatibility: All Major Browsers
Vista-like Ajax calendar is an unobtrusive, slick calendar script which looks and functions similar to the Vista taskbar calendar.
It is built with Mootools and PHP and has datepicker functionality.
The calendar and datepicker have several options for styling and formating them to fit your needs. All properties are optional and reside in a JavaScript object.
Features of this Mootools calendar:
Vista look-and-feel
Quick navigation by switching between months, years and decades without drop-down boxes
Smooth transition animations
Customizable features
Datepicker functionality
Easily changeable date labels (e.g. different languages)
Lightweight (compressed 8,50kB)
Requirements: Mootools 1.11+
Compatibility: All Major Browsers
VCalendar is an open source web calendar application for posting and maintaining events and schedules online, in a calendar format.
VCalendar comes with source code in multiple programming languages: PHP, ASP and ASP.NET (C# and VB.NET).
Some features of this free calendar application:
Localization features with language selectable by end-users (initially English & Russian)
Dynamic CCS (stylesheet) styles, selectable by end-users
Annual, monthly, weekly and daily calendar views
Multiple categories for classifying calendar events
Recurring and all-day events
Role-based user permissions and calendar configuration
Compatibility: ASP, PHP & ASP.NET
Calendars are one of the "musts" in most of the web applications.
Plans is a calendar script which has a simple yet functional interface.
Multi-day event support is one of the rarely found feature that can be found in other calendar applications. Without it, you simply need to hack the logic of the applications.
Another great feature is the powerful recurring events support which makes the administration of the calendar much more easier.
You can also password protect events, create multiple calendars with 1 installation and calendars can share information between each other and even customize the look of every calendar.
To summarize, you should check this calendar application 
.
Requirements: Perl 5.6+
Compatibility: All Major Browsers
MooMonth, is a JavaScript calendar application built with Mootools which is highly configurable an customizable.
With an attractive interface the calendar application has features like:
Day, week, month, *year, and zoom views.
Smooth view transitions.
MooMonth has a powerful function set to be used in creating a feature-rich calendar application.
Although the application is still in alpha it is already very promising.
Requirements: Mootools JavaScript Framework
Compatibility: All Major Browsers
Timeglider is a jQuery plugin for displaying any number of events in a highly-flexible timeline.
Its interface has support for zooming in/out (mouse wheel can be used too) and panning where you can quickly navigate through the time and find events.
Events are clickable and can display a detailed view of them inside a modal box.
JSON is used as the data source for the items in the timeline. Within the data source, it is possible to attach items to categories for filtering them (filtering can also be done keyword-based).
There are also many other features like "the ability to use images in the timeline", "attaching icons to events, "setting an importance for each item" and more.
Requirements: jQuery, jQuery UI
Compatibility: All Major Browsers
wdCalendar is a jQuery plugin that enables us to create an event calendar that functions similar to the popular Google Calendar.
With a drag'n drop interface and feature-rich API, it is possible to create, update or delete events easily.
It has custom views for day, week or month where you can easily go to a selected date (also with the help of provided JS methods).
Usually, multi-day events are complicated, however, wdCalendar handles them well.
P.S. The resource website also shares other useful plugins for a tree menu display, date-picker and more.
Requirements: jQuery
jTrack is a time tracking application that is built with jQuery and works without SQL, sessions or cookies.
It rather uses the localStorage with the help of DOMCached and jquery-json plugins.
The application enables you to add any number of tasks and starts tracking the time for each when a "start" button is clicked.
jTrack is a pretty simple tracker which is suitable to be integrated into other applications or tracking the time in the most plain way.
Also, it is a good resource to see "how localStorage can be used with jQuery".
Requirements: jQuery, DOMCached and jquery-json plugins
Compatibility: All Major Browsers
Any+Time is a feature-rich jQuery plugin (has a PrototypeJS version too) for creating simple-to-advanced date and time pickers.
It can work as a pop-up or an always present picker, can be set as a time or date only picker and supports:
12/24 hour clock
any custom date format
date/time range limits
custom start day of the week
UTC offsets / time zones
and more.
Any+Time can be customized with custom labels and languages. Also, it can be styled completely via CSS or with the help of jQuery UI ThemeRoller.
Using the plugin, you can easily convert dates to/from strings (including JSON and XML) and it supports multiple instances in a single page.
It is keyboard-friendly (WAI-ARIA 1.0) and, optionally, can respond to double clicks.
Requirements: jQuery
Compatibility: All Major Browsers
CalendarPicker is a jQuery plugin that enables us to create a good-looking and pretty original date picker.
It displays a pre-defined amount of the next and previous days/months/years for a quick selection.
Also, users can browse through the dates with mouse-wheel (uses the mouse wheel plugin) or the prev/next buttons.
The date picker can display the current date by default or any selected one on load.
Day and month names can be optionally customized which is nice for multilingual interfaces.
Requirements: jQuery (and, optionally, mouse wheel plugin)
Compatibility: All Major Browsers