Phatsharpie is quite right. If the data in a file is already compressed or very efficiently stored (MP3's, for example) then you will see little of no difference in size, or may actually end up with a slightly LARGER file size.
However, if you are compressing a file format that can be compressed efficiently, such as an image with large areas of a similar colour that can be represented by more efficient math (thus resulting in a smaller final compressed file size), you will find that you have dramatic improvements.
Also be aware that some compression formats may not preserve info you may want to keep about a file. Many of the ZIP format applications destroy info that would be needed (or desired, at least) if you wanted the files to be accessible on OS9. That said, more and more OSX tools are being developed with resource fork and permissions protection as standard these days.