I'll assume that you have the most recent version of QuickTime installed. If not, try upgrading.
If configured properly, the newest versions of QuickTime can play properly encoded and named MPEG-1 media files.
The first step to take to try to fix this issue is to go to QuickTime preferences and make sure it is set up to recognize and play your desired MIME types. This is done by going to System Preferences > Internet & Network > QuickTime.
Once you're in the QT preference panel, click the "Advanced" tab and then click "MIME Settings..." Scroll down the list of MIME categories and click the small triangle by the category entitled "MPEG - MPEG system, video, and audio files".
In the list that follows, scroll down to the bottom and make sure the check box is checked for the category entitled "MPEG media". If it is not, then check that box. This is more than likely your problem. Hit the "OK" button and close the QT preference panel.
Now, launch QuickTime and try playing the file again.
If that does not work, read on.
The next step I would take is to close out all open applications and then run Disk Utility. When DU is finished (it can take a while), restart your computer and try the file again.
If you are still having problems, read on.
Files with the extension ".mpg" usually indicate that you have an encoded media file of the MPEG-1 format. Whereas files with the extension ".mpeg" usually indicate that you have an encoded media file of the MPEG-2 format.
I say usually because sometimes a user may inadvertently change the file extension from "mpg" to "mpeg" ( or vica versa) thinking that they are interchangeable when in fact they are not.
So, after setting the proper QT preferences and running Disk Utility, there are several remaining possibilities why QT cannot play the file:
1. The file may not be encoded properly
2. The file could have corrupt media
3. The file could actually not be a movie file at all
4. The file may have the wrong file extension for the encode format
If one of the above points is the reason that your version of QT cannot play the file, then you only have control over point 4. Rename the file from "mpg" to "mpeg" and try again.
If none of this helps, you can download the VLC player from this site:
http://www.videolan.org/vlc/
Good luck!