Most video/music such as DivX,MP3 are already heavily compressed using optimal algorithms so you will not gain much more compression with something like winzip.
You can, however, reduce the file size by decreasing the quality (video or sound), how much is up to you like my2cents said. Honestly though, this is pain in the ass to do and I would never go this route because once you downsize and delete the original, it's over, you've lost that quality forever and can't go back.
The realistic suggestion is to just get another hard drive (external), they are cheap and you saves the trouble.