Firefox doesn’t support opening Windows executable files (i.e. files with an .exe extension); you have to save it, then manually run it. I missed the ability to execute a program directly from a browser (as Internet Explorer allows).
The OpenDownload add-on fixes that. When you click an executable, the dialog now has a “Run” button, which will cause Firefox to download the program to your system’s TEMP directory, then executes it. Sweet!