A bit more detail to Joachim Sauer's answer:
On Ubuntu at least, the metapackage tomcat6 depends on metapackage tomcat6-common (and others), which depends on metapackage libtomcat6-java, which depends on package libservlet2.5-java (and others). It contains, among others, the files /usr/share/java/servlet-api-2.5.jar and /usr/share/java/jsp-api-2.1.jar, which are the servlet and JSP libraries you need. So if you've installed Tomcat 6 through apt-get or the Ubuntu Software Centre, you already have the libraries; all that's left is to get Tomcat to use them in your project.
Place libraries /usr/share/java/servlet-api-2.5.jar and /usr/share/java/jsp-api-2.1.jar on the class path like this:
For all projects, by configuring Eclipse by selecting Window -> Preferences -> Java -> Installed JREs, then selecting the JRE you're using, pressing Edit, then pressing Add External JARs, and then by selecting the files from the locations given above.
For just one project, by right-clicking on the project in the Project Explorer pane, then selecting Properties -> Java Build Path, and then pressing Add External JARs, and then by selecting the files from the locations given above.
Further note 1: These are the correct versions of those libraries for use with Tomcat 6; for the other Tomcat versions, see the table on page http://tomcat.apache.org/whichversion.html, though I would suppose each Tomcat version includes the versions of these libraries that are appropriate for it.
Further note 2: Package libservlet2.5-java's description (dpkg-query -s libservlet2.5-java) says: 'Apache Tomcat implements the Java Servlet and the JavaServer Pages (JSP) specifications from Sun Microsystems, and provides a "pure Java" HTTP web server environment for Java code to run. This package contains the Java Servlet and JSP library.'
those classes are usually part of servlet.jar
http://www.java2s.com/Code/Jar/wsit/Downloadservletjar.htm
If you've got the Java EE JDK with Glassfish, it's in glassfish3/glassfish/modules/javax.servlet-api.jar.
Have you instaled the J2EE? If you installed just de standard (J2SE) it won´t find.
The normal procedure with Eclipse and Java EE webapplications is to install a servlet container (Tomcat, Jetty, etc) or application server (Glassfish (which is bundled in the "Sun Java EE" download), JBoss AS, WebSphere, Weblogic, etc) and integrate it in Eclipse using a (builtin) plugin in the Servers view.
During the creation wizard of a new Dynamic Web Project, you can then pick the integrated server from the list. If you happen to have an existing Dynamic Web Project without a server or want to change the associated one, then you need to modify it in the Targeted Rutimes section of the project's properties.
Either way, Eclipse will automatically place the necessary server-specific libraries in the project's classpath (buildpath).
You should absolutely in no way extract and copy server-specific libraries into /WEB-INF/lib or even worse the JRE/lib yourself, to "fix" the compilation errors in Eclipse. It would make your webapplication tied to a specific server and thus completely unportable.
Source: Stackoverflow.com