I inherited a Java project in the form of an Eclipse project. After changing the Tomcat configuration (from v6 to v7), Subclipse prompted me to commit the following files:>
I work in a project where we commit the .classpath file since it is very useful that all developers use the same :) If you only use dependencies inside your workspace, this file uses relative paths and thus should be same on all machines. Even if this file might not be necessary to build (with ant e.g.) it´s very convenient to synchronize it.
In contrast the org.eclipse.core.prefs stores (afaik) project-specific, but personal preferences of developers which I would not check in.
With the facets I didn´t work yet in a real project, so I can´t tell. But in general, I think it depends on the information in the file and on the way you work.
If you are unsure, just try it. If you get conflicts in these files all day this is a hint you may not be on the perfect way.