SproutCore distinguishes itself by emphasizing its usage for bringing desktop application functionalities on the web. It’s got a healthy amount of easy-to-follow guides to get you going quickly and its own Google Group for your questions and for interacting with other SproutCore developers.
Spry is Adobe’s Ajax framework. One of the many distinctive features of Spry is its tight integration with Adobe products (such as Dreamweaver, Flash and AIR). Just like any Adobe product, there’s already a ton of documentation to help you get started with Spry quickly.
Archetype demonstration: Slidy Presentation
The June Framework was inspired by the Core library and uses the Module design pattern. For those using MS Visual Studio 2008, you’ll love the documentation that comes with the June Framework because it utilizes Visual Studio’s intellisense format (code hints/auto-completion while you write).
SimpleJS demonstration: you can view the demos in the left side bar of the website under "Functions".
What are you rolling with?