• Windows Zipping for Ms-access by fellow MVP Albert Kallal. Albert's code uses the Info-ZIP freeware dlls.
• Zip a File by fellow MVP Garry Robinson is a "simple way to add a file to a zip file using Access VBA and WinZip"
• Zip file or files with the default Windows XP zip program (VBA)  I don't care for this solution as there is a dependency on the Windows zipping program to be working (it's disabled on my system as I prefer Winzip) as well as VBScript.
• zlib may be an alternative for files such as .gz. 

Statements at the vendors websites and various postings in the Access newsgroups have indicated the following work in Access.   As always your mileage may vary.  Try before you buy.

• Info-ZIP Freeware
         - Sample VB code for using InfoZip
         - More sample code
• Add Zip Compression Libraries
• Xceed Software
• Dynazip
• ZipServer for Windows
   
• Google Computers > Algorithms > Compression
• Google Computers > Software > Data Compression

File Compression using the OS and NTFS file system

See Visual Basic > Files Directories Drives - Compress-uncompress an file or directory for sample code.   See File Compression and Decompression (Windows) for more details.  All you need to do is to set the compression state of the file and the OS will compress the file for you.

Note that I haven't tested this code myself.