<p>My C(++) program, written and compiled using Visual C(++)/Visual Studio, runs fine on my own machine, but refuses to run on another machine. The error message I get is "This application has failed to start because the application configuration is incorrect. Reinstalling the application may fix this problem."</p>

If you write a C++ program, it links dynamically to the C Runtime Library, or CRT for short. This library contains your printf, your malloc, your strtok, etcetera. The library is contained in the file called MSVCR80.DLL. This file is not by default installed on a Windows system, hence the application cannot run.
The solution? Either install the DLL on the target machine through VCREDIST.EXE (the Visual C++ Redistributable Package), or link to the CRT statically (plug the actual code for the used functions straight into your EXE).
Distributing and installing VCREDIST along with a simple application is a pain in the arse, so I went for the second option: static linking. It's really easy: go to your project's properties, unfold C/C++, click Code Generation, and set the Runtime Library to one of the non-DLL options. That's all there is to it.