Babel
Babel is a compiler for writing next generation JavaScript.
Respond
A fast & lightweight polyfill for min/max-width CSS3 Media Queries (for IE 6-8, and more)
HTML5shiv
This script is the defacto way to enable use of HTML5 sectioning elements in legacy Internet Explorer.
ES5 Shims
ECMAScript 5 compatibility shims for legacy JavaScript engines
Es6 Shim
ECMAScript 6 (Harmony) compatibility shims for legacy JavaScript engines
Yepnope.js
An Asynchronous Conditional Resource Loader
Store
A better way to use localStorage and sessionStorage
CSS3 Pie
A behavior for Internet Explorer allowing it to recognize and render various CSS3 box decoration properties
Selectivizr
Selectivizr is a JavaScript utility that emulates CSS3 pseudo-classes and attribute selectors in Internet Explorer 6-8.
Placeholders.js
A JavaScript polyfill for the HTML5 placeholder attribute
Svgeezy
Allows for automatic Image fallbacks for browsers that can't handle SVGs
Flexie
Legacy support for the CSS3 Flexible Box Model
Augment.js
Modern JavaScript in your IE
Poly
Small, fast, awesome. The only ES5-ish set of polyfills (shims) you can mix-and-match because they're individual AMD modules.
CSS Parent Selector
CSS4 parent selector based on jQuery
Css3 Finalize
Tired of adding prefix for each broswer when it comes to the new css3 attributes?
Hitch
A lightweight engine that allows you to hitch new capabilities to the browser (prollyfill).