The Google Libraries API and Microsoft Ajax Content Delivery Network (CDN) hosts the popular jQuery library and enables you to easily add them to your Web applications. For example, you can start using jQuery which is hosted on this CDN simply by adding a <script> tag to your page that points to a CDN link. These CDN's are very efficient and reliable as they have more replications to reduce latency. Browsers limit the number of concurrent connections (file downloads) to a single domain so using CDN's triggers parallel downloads leading to faster page loading. Here are some reasons to USE and NOT USE the CDN networks.
The versions of jQuery keeps getting updated every now and then and it's difficult to keep track of the latest releases. For that reason I've created a page that automatically pulls in the latest versions and links for the jQuery, jQueryUI and jQueryUI Theme libraries for both Google and Microsoft CDN's. Keep it bookmarked to stay up-to-date on jQuery releases.