As the website says: jquery is the Swiss Army knife of javascript - it's small, versatile, and has almost zero learning curve
, and 15 Days Of jQuery covers varied and popular tasks such as Ajax requests, inline editing, multiple file upload and accessible unobtrusive JavaScript tabs.
The idea behind jquery is that it is a lightweight library that can do many of the UI things people are looking for. As a vote of confidence, it was chosen as the JS library for Drupal.
Dustin Diaz comes out with DED|Chain, a library that provides the ability to chain ala jQuery but with the Yahoo! UI. It's early days, but it looks interesting, simple and easy (or as he says: Fun!).
Having taken a year to develop, Dojo looks to be an interesting new Open Source Ajax and DHTML toolkit. They have a mailing list, wiki and IRC node for support. Be sure and check out the "Slideshow Widget Example".