We started to work on some projects, and after getting the source code, we could not use the web projects in eclipse because they were not defined as Eclipse Dynamic Web projects. Here is a small trick to convert these general projects to Dynamic Web projects.

First change your perspective to Resource and check your .project file if natures tag also contains facet nature:

    <natures>
        <nature>org.eclipse.jdt.core.javanature</nature>
        <nature>org.eclipse.wst.common.project.facet.core.nature</nature>
    </natures>

And second update your project facets by Project Properties/Project Facets/Add Remove Project Facets:

So you can use and add this new web project to Tomcat server.

Note: We still use older Eclipse version 3.2.2 because of some custom plugin problems