It is not a new problem but as someone asked me how to correct it, I decided to write the solution.
After the installation of ASP.NET AJAX 1.0 Extensions on a machine with Visual Studio 2008, we could think that we will find a ASP.NET AJAX Enabled Web Application template but it is not the case as you can see on the following picture:
As we do not have any other choice, we have to select the ASP.NET Web Application. In the toolbox, we can see some the basic components from ASP.NET AJAX Extensions. Great!

It is really easy to use them with a simple drag and drop from the toolbox to the web page designer.
As soon as we dragged the first component, some changes are persisted to web.config file (the easier way to see this is to have the web.config oprened in Visual Studio during the operation, you will be notified about changes):
<assemblies>
<add assembly="System.Web.Extensions, Version=1.0.61025.0,
Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>
</assemblies>
So we can think that everything is already as Visual Studio did everything thing for us. When the page is run, Sys is undefined error message appears in the browser.
Why this? The answer is quite simple. In the HTML page source, we can find:
<script src="/ScriptResource.axd?d=xyz" type="text/javascript"></script>
<script src="/ScriptResource.axd?d=abc" type="text/javascript"></script>
If we can and paste the url, we can have a look to the file content. But this url does not exist. In fact, the server does not know what to do with the .axd extension that is why we have to add the following content in the web.config between <system.web> and </system.web>:
<httpHandlers>
<add verb="GET" path="ScriptResource.axd" type="System.Web.Handlers.ScriptResourceHandler"
validate="false"/>
</httpHandlers>
Now, you can develop applications using AJAX and the only limit is your imagination.
Minimal web.config:
<?xml version="1.0"?>
<configuration>
<appSettings/>
<connectionStrings/>
<system.web>
<httpHandlers>
<add verb="GET" path="ScriptResource.axd" type="System.Web.Handlers.ScriptResourceHandler"
validate="false"/>
</httpHandlers>
<compilation debug="false">
<assemblies>
<add assembly="System.Web.Extensions, Version=1.0.61025.0, Culture=neutral,
PublicKeyToken=31BF3856AD364E35"/>
</assemblies>
</compilation>
<authentication mode="Windows"/>
</system.web>
</configuration>
You can find a complete web.config file by accessing the following path:
C:\Program Files\Microsoft ASP.NET\ASP.NET 2.0 AJAX Extensions\v1.0.61025.