I'm using YUI for a few of their controls (DataTable, Paginator, TabView, Autocomplete, etc.) since they work out of the box with very little coding. But for most everything else I rely on jQuery for it's simplicity.

I'm hoping in the future jQuery will have an equivalent set of controls so I can stick to a single framework.

• YUI for a complete, professional looking, enterprise oriented widget toolkit.
• Prototype if you are using http://script.aculo.us/ or like the Ruby way of doing things.
• jQuery has gotten very popular and is most probably your best bet if you code in ASP.NET
• You can't go wrong with either Dojo or MooTools

Being a Dojo developer I would recommend Dojo. While my choice is not surprising, I became a Dojo developer because I found following things, which are done better than in other JavaScript frameworks:

• OOP (and other paradigms) done right.
• Widget infrastructure done right.
• Modules done right with all necessary goodies:
  • Lazy loading of modules dynamically.
  • Possibility to extract only necessary modules and build a custom one-file profile.
  • Asynchronous loading of modules if desired.
  • Simple integration with CDNs for heavy-duty web applications.
• Sheer breadth of available modules in DojoX including graphics, charting, grids, and so on.
• Ability to use it in non-browser environments.
• Attention to details in widgets:
  • support for i18n (including LTR and RTL languages),
  • support for l10n (including standard date, currency, number formatting),
  • provisions for people with special needs (automatic high-contrast mode, keyboard-only support, and so on) — useful for regular users too, and mandatory for most government contracts.
• Smart people in the community (last but not least) — as much as I love hand-holding for novices at some point every developer becomes "seasoned" and needs much more than that.

If all you want is to write one-liners and add simple progressive enhancements to existing web applications, you can do it with pretty much any framework, or even with a pure JavaScript. But as soon as your web application becomes bigger or more complex good packaging, good support for your favorite methodologies, good building blocks, and the ability to make your own building blocks become more and more important. That's why I settled on Dojo, and never looked back.

I think you might find JQuery is rapidly catching up on the plug-ins front.

Jquery

• Fast
• Well documented
• Easy to use
• Chaining
• Unlike prototype it doesn't extend an object if you didn't specifically ask for it (try looping an array in prototype)
• easy-to-use AJAX (I love the $.ajaxSetup() function)
• Nice Event handlers
• CSS selectors
• filtering your selection
• did I mention chaining?
• Small (only 30kb)
• Nice little build-in effects.
• Plugins

If you are doing anything really javascript-heavy, like a single-page site i would say dojo, because of it's great architecture, templates, widget-system and built in widgets for pretty much everything. Otherwise, if you need more lightweight style, i would say jQuery :)

I use YUI because I think it is complete in functionality.

The YUI 3.0 will be very like jQuery in its strengthness.