<p>I have the .net framework 3.5 on my development machine and also am using the AJAX toolkit  in my code.  In order to publish this code to a server for my users, do I need anything on the server in order for my AJAX code to operate correctly? </p>

You need only the .NET framework 3.5.
If you publish your project, the AJAX Toolkit used will be also copied over. If you only reference the AJAX Toolkit via file, not via project, then be sure you set the dll to "Copy always" in the properties window.