Out of the box, my FC4 does not play MPEG videos. When I use FireFox to browse to a sample video, I tell FireFox to open it in the default application, Totem. Totem runs, and a window appears, complaining that it doesn't know how to decode the file.
To install MPEG video support for Totom, I type:
$ sudo yum install gstreamer-plugins-extra-video
After that, it just works.