Since this is a library supposed to be used with other applications there
is not very much in ways of a flashy demonstration available. Still there are
two small example applications:

1.) Example, which is exactly this, an example of some of the basic functions
    of Zlib. If it works, you can be confident the program has been built 
    correctly.
    
2.) Minigzip, which is a bare bones proof-of-concept implementation of Gzip 
    using Zlib. Since this does need to write files, a example is copied 
    to sys$scratch, and compressed/decompressed there.    

These tests can be invoked using the provided freeware_demo.com