It depends on how old the .exe file is. If it is a DOS program, DOSbox can run it. If DOSbox comes back with "this program was written for Microsoft Windows", then you can use the ideas that GGJstudios gave. If you don't want to pay for CrossOver, it is just a commercial implementation of Wine, which you can get for free.
I can think of one no-cost option for you, but you use up over a gig of disk space on a windows iso image, and several more gig of disk space on a windows virtual drive full of windows and all its windows-ish files...
1) download virtualbox
2) download win 8 preview
3) run the exe file inside win 8 running inside a virtualbox
(you will have to "install" win 8 in a virtualbox which takes a while but it is free)
There is another, not quite free option for you.
1) download crossover (shareware)
2) run the exe in crossover's win 2000 virtual machine
(a small percentage of windows programs work in crossover)
There is a third, more costly option for you.
1) purchase an oem copy of win 7 for about $100 (while you still can)
2) purchase parallels (not free but comes with ready to use images for win 8 preview and a few others including linux) or use virtualbox (free)
3) if you set up a win 7 virtual machine in parallels, still using a virtual drive the integration is much nicer than that available in virtualbox.