I use a Mac and have QuickTime 5. It will play almost all mpg (mpeg) and most avi. For the problem avi, I use DivX Doctor II. It will fix audio (if there seems to be none) and video (if you see a white screen). It's a simple drag-and-drop application. There are many threads here in the forums regarding this program. Do a search here for "avi" or "Divx" and you should be able to get some help there. As for mpgs that just don't even start to run, well... I just trash them.
If you have those "larger" mpgs that only play for one minute, then you should try Rosetta. It's a $15 (or is it $10?) shareware fee, but very easy to use. It will split the video and then you can paste it back together. I had tried bbDEMUX, but that splits it into two different files - an audio file and a video file that you have to try to get going at the same time. Sucked. I've had no problems with Rosetta. It's worth the $. In my opinion.
Do a Google (or whatever) search for "Rosetta" and "DivX Doctor II" and check them out.
Hope this helps.