AuraJS is a component framework that lets you build fully functional web applications with ease. In AuraJS, everything is a component — “An Aura component represents a unit of a page. An independent block of reusable code, wrapped up so that it works well on its own or together with other components.”
AuraJS comes with its own custom set of extensions as well. You can use it in assonance with other popular MVC frameworks, such as AngularJS.
Kraken is powered by Gulp.js and is both flexible and modular.
Stapes.js is just 2 KB when minified and barely 600 lines of code.
Spine has also been well-documented, and is backed by screencasts to help you get a better idea of its working.
Skel is flexible, and also has an SASS based implementation of itself.
The name speaks for itself — Responsive is a framework that you will use for building, well, responsive websites. It is accessible, flexible, and can be extended to suit your needs and requirements.
Responsive is simple and lightweight — the final minified file is just 23 KB in size, and it is not bloated like many other frameworks out there. Responsive, as a framework, gives you a skeleton-approach to your projects, with all the bloated fluff removed and leaving you with a no-nonsense framework.
scaleApp also supports server-side scripts such as Node.js
Chibi is not something you might be able to use for complex projects, such as animations (though you can make it work in assonance with CSS transitions).
Tupai.js supports packages, functions, variables and classes, and comes with an MIT License.