To view the architecture of your system, right click in the lower left corner of the screen where the Start Screen would be launched and select System from the list of administrative tools. Under the System category the architecture will be listed under System type. Depending on the architecture of the application you are trying to run, you may need one architecture or another.
16 bit applications, like DOS applications, require Windows 8 32 bit and for 16 bit support to be enabled. Upon first launching a 16 bit application you may be prompted to enable 16 bit support. If you are not prompted, it can also be enabled and disabled in the Control Panel.
32 bit applications will run in both 32 bit and 64 bit architectures of Window 8.
64 bit applications require Windows 8 64 bit. To change Windows between architectures the operating system must be reinstalled in a clean installation from media of the appropriate architecture.
If the application is of the correct architecture but still will not install, you may want to
try running in Compatibility Mode which will attempt to mimic the operating system the application was designed for. Beyond that the Application Compatibility Toolkit (ACT) and customizable shims come into the picture or editing of .msi files with Orca depending on the installation package.
More on Application Compatibility can be found here at the Springboard Series on TechNet.