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