Monkey Raptor

Recommended FREE Public CDN
CDN : Content Delivery Network.

A content delivery network or content distribution network (CDN) is a large distributed system of servers deployed in multiple data centers across the Internet.
Wikipedia

Speed up your AJAX (Asynchronous  JavaScript and XML) applications with these.

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Google's CDN

Widely used on the internet. Hosts JavaScript libraries (and CSS files for jQuery UI and jQuery Mobile - basic theme) :

• AngularJS
• Chrome Frame
• Dojo
• Ext Core
• jQuery
• jQuery UI
• jQuery Mobile
• MooTools
• Prototype
• script_aculo_us
• SWFObject
• Web Font Loader

Go to Google's Hosted Libraries

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Microsoft's CDN

Hosts JavaScript libraries and CSS files of the following :

• jQuery
• jQuery Migrate
• jQueryUI
• jQuery Validation
• jQuery Mobile
• jQuery Template
• jQuery Cycle
• jQuery DataTables
• Modernizr
• JSHint
• Knockout
• Globalize
• Bootstrap
• ASP.NET Ajax
• ASP.NET Web Forms
• ASP.NET SignalR
• ASP.NET MVC
• AJAX Control Toolkit

They also generously provide fallback method of switching between CDNs.

Go to Microsoft Ajax CDN

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CDNJS

Powered by CloudFlare. Hosts everything. JavaScript libraries, CSS libraries, SWF objects, images (UI icons) and even moar! You can also submit your libraries.
Tons of awesomeness-es. You can find any library you might need and it will be delivered with lightning speed. No problem for cross-domain thingy.

For instance, they already have libraries for :

• jQueryUI  (JS and CSS)
• SyntaxHighlighter (JS and CSS)
• PrefixFree (JS)
• Normalize (CSS)
• Reset (CSS)
• Modernizr (JS)
• Twitter Bootstrap (JS and CSS)
• Prettify (JS and CSS)
• MathJax (JS and images) 
• Social Likes (everything, JS, JSON, CSS, images, etc)

And still many, many moar!