If you've ever messed around with Linux, you're probably familiar with a little program called "Wine," WINdows Emulator/Wine Is Not an Emulator. With its magic, you can run Windows applications on your Linux box, and soon, Wine could be running them on your Android phone as well.
Alexandre Julliard, the original developer behind Wine, has now shown off a preliminary build of Wine for Android this Sunday in Brussels. So far, the Android version of the emulator has been subpar; Phoronix went so far as to describe the demo's performance as "horrendously slow," but demo was run on an emulated Android device. Theoretically the performance should be much better on an actual phone or tablet, and after it's had a bit more development time.
All in all, a workable version of Wine for Android is still a long way off, but this proves that if nothing else it's at least possible, and by extension, so is running real Windows programs on your phone, so long as your phone powerful enough.