document.createElement("script") synchronously

You can create your <script> element with an "onload" handler, and that will be called when the script has been loaded and evaluated by the browser.

var script = document.createElement('script');
script.onload = function() {
  alert("Script loaded and ready");
};
script.src = "http://whatever.com/the/script.js";
document.getElementsByTagName('head')[0].appendChild(script);

You can't do it synchronously.

edit — it's been pointed out that, true to form, IE doesn't fire a "load" event on <script> tags being loaded/evaluated. Thus I suppose the next thing to do would be to fetch the script with an XMLHttpRequest and then eval() it yourself. (Or, I suppose, stuff the text into a <script> tag you add; the execution environment of eval() is affected by the local scope, so it won't necessarily do what you want it to do.)

edit — As of early 2013, I'd strongly advise looking into a more robust script loading tool like Requirejs. There are a lot of special cases to worry about. For really simple situations, there's yepnope, which is now built into Modernizr.

This isn't pretty, but it works:

<script type="text/javascript">
  document.write('<script type="text/javascript" src="other.js"></script>');
</script>

<script type="text/javascript">
  functionFromOther();
</script>

Or

<script type="text/javascript">
  document.write('<script type="text/javascript" src="other.js"></script>');
  window.onload = function() {
    functionFromOther();
  };
</script>

The script must be included either in a separate <script> tag or before window.onload().

This will not work:

<script type="text/javascript">
  document.write('<script type="text/javascript" src="other.js"></script>');
  functionFromOther(); // Error
</script>

The same can be done with creating a node, as Pointy did, but only in FF. You have no guarantee when the script will be ready in other browsers.

Being an XML Purist I really hate this. But it does work predictably. You could easily wrap those ugly document.write()s so you don't have to look at them. You could even do tests and create a node and append it then fall back on document.write().

This is way late but for future reference to anyone who'd like to do this, you can use the following:

function require(file,callback){
    var head=document.getElementsByTagName("head")[0];
    var script=document.createElement('script');
    script.src=file;
    script.type='text/javascript';
    //real browsers
    script.onload=callback;
    //Internet explorer
    script.onreadystatechange = function() {
        if (this.readyState == 'complete') {
            callback();
        }
    }
    head.appendChild(script);
}

I did a short blog post on it some time ago http://crlog.info/2011/10/06/dynamically-requireinclude-a-javascript-file-into-a-page-and-be-notified-when-its-loaded/