How do I combine WebResource.axd and ScriptResource.axd files so as to result in less requests to my ASP.NET server?

As the others have stated, using the ASP.NET AJAX Toolkit's ToolkitScriptManager rather than the default ASP.NET ScriptManager will allow you to do some script combining, including your own scripts embedded as resources - there's a good post about it at Script combining made easy.

If you have the luxury of using ASP.NET 3.5 SP1, then there are some further additions to the ASP.NET ScriptManager that allow you to combine a lot more scripts, including general .js files in your solution into one script call.

Check out the video here:

Using Script Combining to Improve Performance

Try using ajax - ToolkitScriptManager instead of asp - ScriptManager - it tends to combine as much of the resource requests as it can.