It's not the files themselves. It's the directory where you keep the files.
You can chmod your files 444 if you want (assuming you just want to read them). You can set (also, as long as you just want to read, the ownership of the files to anything, such as nobody, bofh, etc). However. The user your web server is running as, must own the directory and have full access there.
This means you should chown and chmod the directory where the files are in to at least apache.someone (if apache is the user your web server is running as) with the permission 700 (though 755 is more common and better for plenty of reasons).
And, that, if you do it right, is it.
Hope that helps
/j.