We use the JQuery library and write our own code. We’ve also used some snippets from  mootool’s a few times. 

I’ve used YUI but it is difficult to implment without implmenting it for everything in your website.  MEaning your CSS framework and Javascript.  I may not be as good as other webmasters, but implementing anoter framework in addition to YUI would be overkill.  YUI can do everything but it’s not always the ideal solution.
YUI has a lot of dependencies.  I’ve implemented Prototype on another website of mine which is an EXCELLENT javascript framework that is easy to use and implement. It’s also open source, yippe!

Lemme start it off!!
YUI/RICO/Mootools/Scriptalishousssouss or just the low lever coding straight from the prototype.js it’s self?
What’s your preference?
All the ”bundled” script(s) are nice but damn do they carry a hefty file size.