As others have said, you're missing the server api jar.
Having said that, downloading just the servlet api jar and not the server that goes with it means that you can't actually test your code.
In Eclipse, once you're installed a servlet container, such as Sun's Glassfish, Apache Tomcat, or Jetty, you can create a server instance of it so that Eclipse will compile against your server's servlet implementation. Creating a server instance also means that Eclipse's Run on Server command works.
IBM has a slightly outdated guide on Developing Web applications with Tomcat and Eclipse. The entire "Install the Web tools" section can be skipped if you have the Eclipse EE version, as Web Tools are already installed.