Handy safety tip: to create a RESTEasy-friendly Maven project in Eclipse, do the following:

1. Create the project as a simple Maven project
2. In the project Properties -> Project Facets, make the project faceted, and select "Dynamic Web Module" (you may get a NullPointerException, but it doesn't seem to matter). Under "Further Configuration...", point the WebApp directory to be src/main/webapp, and have it create the web.xml file.
3. Under "Web Content Settings", set the Context root
4. Under "Deployment Assembly", select "Add...", select "Java Build Path Entries", and select "Maven Dependencies". It should put them in WEB-INF/lib.
5. Add the code and the dependencies to the pom.xml. Make sure to add the RESTEasy stuff to the web.xml file.

You should be able to deploy it from Eclipse into Tomcat without any issues