I'm getting the following error when I try to run a simple JSP program on Tomcat in Eclipse.
Several ports (8005, 8080, 8009) required by Tomcat v6.0 Server at localhost are already in use. The server may already be running in another process, or a system process may be using the port. To start this server you will need to stop the other process or change the port number(s).
How is this caused and how can I solve it?
You've another instance of Tomcat already running. You can confirm this by going to http://localhost:8080 in your webbrowser and check if you get the Tomcat default home page or a Tomcat-specific 404 error page. Both are equally valid evidence that Tomcat runs fine; if it didn't, then you would have gotten a browser specific HTTP connection timeout error message.
You need to shutdown it. Go to /bin subfolder of the Tomcat installation folder and execute the shutdown.bat (Windows) or shutdown.sh (Unix) script. If in vain, close Eclipse and then open the task manager and kill all java and/or javaw processes.
Or if you actually installed it as a Windows service for some reason (this is namely intented for production and is unhelpful when you're just developing), open the services manager (Start > Run > services.msc) and stop the Tomcat service. If necessary, uninstall the Windows service altogether. For development, just the ZIP file is sufficient.
Or if your actual intent is to run two instances of Tomcat simultaneously, then you have to configure the second instance to listen on different ports. Consult the Tomcat documentation for more detail.