There are three versions of Windows 8. For more details, see "What is the difference between Windows 8 Pro and Windows RT".
Windows 8 and Windows 8 Pro have the new Metro interface, but also have the old Windows 7 style desktop. These OSes will be compatible with almost any Windows software.
Windows RT has only the new Metro interface, with very limited desktop support for a few built-in apps. Generally, only new apps will run on this version.
To figure out if your application will run on your Windows 8 device, first determine which version of Windows you have. If you aren't sure, try getting to the desktop. If you're able to get to the desktop, press Windows Key + R, and type
winver, then hit enter. This will display your Windows version. If you're unable to get to the desktop, you probably have Windows RT.
If you have Windows 8 or Windows 8 Pro:
Any program in the Windows Store will work on these versions of Windows. All Metro apps will be supported. You can also run most legacy Windows applications. Any program that runs on Windows 7 should run on Windows 8, unless it's a low-level program such as certain interface customization programs.
If you have Windows RT:
Any Metro app in the Windows Store will run. Legacy applications will not work unless the developers have created a specific Metro version. If your program worked in Windows 7, it probably will not work on Windows RT.