We can do that with earlier version of Tomcat. Read about invoker servlet. But its a sin. Check out Javaranch FAQs. [ April 16, 2005: Message edited by: Adeel Ansari ]
As Adeel said, Tomcat used to ship with an invoker servlet that allowed you to enter the package and class name of the servlet. It turned out to be a disaster (see link in Adee's post) and has been disabled in recent versions.
The commented out configuration lines can be found in TOMCAT_HOME/conf/web.xml.