Before mplayer-gui installation in Fedora Core 12, you will have to add RPM Fusion repositories. After that, yum will resolve all dependencies and mplayer will be installed in a minute.
How to add RPM Fusion repositories?
# add RPM Fusion repository with the rpm command rpm -Uvh http://download1.rpmfusion.org/free/fedora/rpmfusion-free-release-stable.noarch.rpm rpm -Uvh http://download1.rpmfusion.org/nonfree/fedora/rpmfusion-nonfree-release-stable.noarch.rpm
If you have proxy problems, please use --httpproxy switch in rpm command. If you still have problems, you can manually download free and nonfree repositories and then install them from the local directory:
rpm -Uvh rpmfusion-free-release-stable.noarch.rpm rpmfusion-nonfree-release-stable.noarch.rpm
Detailed information about configuring RPM Fusion repositories can be found at http://rpmfusion.org/Configuration page. Finally, Fedora Core 12 is ready for mplayer-gui, xine or vlc installation.
yum install mplayer-gui yum install xine yum install vlc
And small issue before the end. Instead of playing AVI, mplayer gave me the following message:
Error opening/initializing the selected video_out (-vo) device
The solution was to change output video device in mplayer-gui to xv, gl, ... (depends on your video hardware but in general, xv should work):
mplayer-gui -> Preferences -> Video -> xv
Cheers!
06/06/2010 - This tutorial also works for Fedora 13
12/28/2010 - This tutorial also works for Fedora 14
04/14/2012 - This tutorial also works for Fedora 16
05/31/2012 - This tutorial also works for Fedora 17
01/23/2013 - This tutorial also works for Fedora 18 (with some tweaks on How to install mplayer in Fedora Core 18)

@Prabhu - I assume that you try to add RPM Fusion repositories for FC14 but your system is not FC14. First, you can try the following command:
... to see what is your system version. Here is output from my PC:
Anyway, repository installation with following command:
should resolve version issues and install without a problem. On the other hand, if you need to manually download/install rpmfusion-free-release package, make sure your system release and package release are matched.
Thanks so much, this was really helpful!
The above steps also work for Fedora 16
thanks
p
@the Peak Oil Poet - This is very useful information - thank you!