Not at all sure I understand the question; if you're asking if there's a way to take an existing .mpg file, and compress it into something smaller, like a .zip archive, then the answer of the poster above applies to you. There's not much point, though, since the video won't get any smaller even if you do compress it.
If you're trying to CREATE an .mpg file, there are several other threads in this forum asking the exact same question. It's not all that easy, but there are some tools that will do it (ffmpeg is one of them).
If you're trying to take an .mpg file and compress it into a different kind of video (like an .avi -- DivX or something), there are many free and shareware tools for doing it (again, ffmpeg is a good one).