The mechanism to determine what goes in the war is not the build path as for "normal" applications, but the "Deployment assembly".
Right-click on the root node of the dynamic web project, and select Properties, and select Deployment assembly. Here you can add projects (which are jarred up and added to WEB-INF/lib) and individual jars in the project.
EDIT 2015-08-20: A few years later, Maven has become the standard way to build Java-based software primarily due to the script based approach to dependency management. This includes how to build WAR-files, and the three major IDE's (IntelliJ, Netbeans and Eclipse) fully support this allowing you to switch between IDE's while developing. In Eclipse the problem asked here will not apply, as this is fully controlled by the Maven plugin.
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