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Peyote said:

hmm. I don't think that helps.

Were these applications built for the Macintosh, or are they for normal PC systems. An EXE extension at the end of a file name, is simply that, an extension. Some programs built for OS X do contain the .EXE extension, Folding@Home comes to mind as one of them.

What is the application?
 
Some .exe files are zip archives packaged in a way for Windows to auto-unzip them. Such files may be opened on a Mac by first changing the extension from .exe to .zip and then opening them with Stuffit Expander.

This worked for me when I downloaded .exe files of WMV HD trailers and opened them on my Mac. To get smooth playback I exported the WMV files to DVCProHD (using Flip4Mac to open the WMV files in QuickTime Player).
 
.exe files are windows applications.

Some self extracting zip files are .exe, but the .exe format is a Windows Executable. So it won't run on a Mac (except by the method mentioned above if it is actually a zip file).
 
Commercially, the only viable product to open windows programs is Virtual PC. There are a few free open-source projects that seek to replace VPC, but they aren't quite there yet.

Often, however, you can find Mac(aqua/classic)/UNIX(x11) versions of programs. VPC, as an emulator, is slow, so you'll probably find that it is best to find a native way of doing things.

As others have mentioned, .exe files can be self-extracting .zip files. These can be handled without VPC.
 
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