Where do you include the jQuery library from? Google JSAPI? CDN?

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>

If you want to use Google, the direct link may be more responsive. Each library has the path listed for the direct file. This is the jQuery path

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.1/jquery.min.js"></script>

Just reread your question, is there a reason your are using https? This is the script tag Google lists in their example

<script src="http://www.google.com/jsapi"></script>

One reason you might want to host on an external server is to work around the browser limitations of concurent connections to particular server.

However, given that the jQuery file you are using will likely not change very often, the browser cache will kick in and make that point moot for the most part.

Second reason to host it on external server is to lower the traffic to your own server.

However, given the size of jQuery, chances are it will be a small part of your traffic. You should probably try to optimize your actual content.

jQuery 1.3.1 min is only 18k in size. I don't think that's too much of a hit to ask on the initial page load. It'll be cached after that. As a result, I host it myself.