Without a doubt I choose to have JQuery served by Google API servers. I didn't go with the jsapi method since I don't leverage any other Google API's, however if that ever changed then I would consider it...
First: The Google api servers are distributed across the world instead of my single server location: Closer servers usually means faster response times for the visitor.
Second: Many people choose to have JQuery hosted on Google, so when a visitor comes to my site they may already have the JQuery script in their local cache. Pre-cached content usually means faster load times for the visitor.
Third: My web hosting company charges me for the bandwidth used. No sense consuming 18k per user session if the visitor can get the same file elsewhere.
I understand that I place a portion of trust on Google to serve the correct script file, and to be online and available. Up to this point I haven't been disappointed with using Google and will continue this configuration until it makes sense not to.
One thing worth pointing out... If you have a mixture of secure and insecure pages on your site you might want to dynamically change the Google source to avoid the usual warning you see when loading insecure content in a secure page:
Here's what I came up with:
<script type="text/javascript">
document.write([
"<script src='",
("https:" == document.location.protocol) ? "https://" : "http://",
"ajax.googleapis.com/ajax/libs/jquery/1.2.6/jquery.min.js' type='text/javascript'></script>"
].join(''));
</script>
UPDATE 9/8/2010 -
Some suggestions have been made to reduce the complexity of the code by removing the HTTP and HTTPS and simply use the following syntax:
<script type="text/javascript">
document.write("<script src='//ajax.googleapis.com/ajax/libs/jquery/1.2.6/jquery.min.js' type='text/javascript'></script>");
</script>
In addition you could also change the url to reflect the jQuery major number if you wanted to make sure that the latest Major version of the jQuery libraries were loaded:
<script type="text/javascript">
document.write("<script src='//ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js' type='text/javascript'></script>");
</script>
Finally, if you don't want to use Google and would prefer jQuery you could use the following source path (keep in mind that jQuery doesn't support SSL connections):
<script type="text/javascript">
document.write("<script src='http://code.jquery.com/jquery-latest.min.js' type='text/javascript'></script>");
</script>