If the exe is your code then there are several things you can do.
As Bruno Rohée said: Everyone give him an upvote.
You can and should sign Windows applications : see http://msdn.microsoft.com/en-us/library/ie/ms537361(v=vs.85).aspx
You can try to obfuscate your code using a tool for whatever language you created the application in. This technique will attempt to break (hard to do) decompilers and analysers from constructing readable code from your EXE.
You should mark the file on your server as read-only for all users and change the owner to an account that isn't controllable by any infection vector so that if your web-server gets infected with something it can read but not write to the file. Essentially
chmod 644 the file.
You can submit it to and link to https://www.virustotal.com/ and ask your users to do the same. virustotal.com will run the file through a bunch of virus scanners and give you a report.
Which is similar to the "trust me approach" but now you're backing your claim.
Additionally you should post your hashsum's on the download page.
The best way to prevent modification to your code is by signing it. If a signature is broken on your EXE you know that your Windows user will know about it.
You can also Flag your application at compile time to run Address Space Randomization. This means that for a cracker trying to exploit your application it will load itself into random parts of memory instead of 'in a straight line', similar to obfuscation.
Edit: I said the best way to prevent modification of your code, that is incorrect. I should have said that the most transparent way to alerting users of modified code.