You have to set the runtime for your web project to the Tomcat installation you are using; you can do it in the "Targeted runtimes" section of the project configuration.
In this way you will allow Eclipse to add Tomcat's Java EE Web Profile jars to the build path.
Remember that the HttpServlet class isn't in a JRE, but at least in an Enterprise Web Profile (e.g. a servlet container runtime /lib folder).