Libraries
Two approaches
Understand how the library works and use it to save time and effort.
Use a library like a black box that you dare not mess with.
Like any tool, a library could be used for good or for evil.
Prototype
http://prototype.conio.net/
Lots of useful shortcuts, including Ajax
Clean code, quite lightweight
Little or no documentation
Comes bundled with Rails... but obtrusively
Script.aculo.us
http://script.aculo.us/
Built on top of Prototype
Lots of animations and effects: fades, drag'n'drop, etc.
DHTML by any other name
You can cherry pick the files you need
Ongoing documentation by users
Moo FX
http://moofx.mad4milk.net/
Like script.aculo.us, built on top of Prototype
Very lightweight
Effects built on width, height, and opacity e.g. show/hide, fade, etc.
Rico
http://openrico.org/
Yet again, built on top of Prototype
Ajax, animation, and drag'n'drop
Documentation is sparse and what's there encourages obtrusive JavaScript.
jQuery
http://jquery.com/
A compressed version is provided to keep the filesize down
Chainable methods: uses dot syntax to join multiple methods
Handy for attaching events and some visual effects
Mochikit
http://www.mochikit.com/
Very well documented
Quite geeky: borrows ideas from other languages like Python
You can cherry pick the files you need
Dojo
http://dojotoolkit.org/
Well documented
Quite complex: it will make most sense to "serious" programmers
The Ajax functionality uses JSON
Geared towards creating widgets
Sarissa
http://sourceforge.net/projects/sarissa
Designed to make parsing XML easier: XSL, XPath, etc.
Worth investigating if you use XML a lot
Geeky: not for the faint of heart
Yahoo! UI Library
http://developer.yahoo.com/yui/
Well researched and documented
Modular
Also provides widgets (sliders, calendars, etc.)
Design patterns
also open-sourced.
Conclusions
Choose a library to suit your needs: don't adjust your needs to fit the way a library works.
If you use a library, understand how it works so that you aren't clueless when something goes wrong.
Remember the end user: a library might make your life easier, but at what cost? (filesize, browser compatibility, etc.).
Thank you