The other guys were slightly right. You don't need the servlet  api lib
to run a servlet, but you sure as hell need it to compile a servlet.
The jar you should include in your project  lib path  is usually called
servlet,jar (you should find it in thejakarta-servletapi-4/lib directory.
It's best to use the same version of servlet api to compile with as you
will deploy with, just to avoid confusion.
If you are using tomcat - the servket api lib will be in
tomcat_dir/common/lib/servlet.jar.