I understand the difference between the two architectures is the separation of instructions from data in the Harvard architecture. But how do I know which type of system I'm on? Is it possible to write a program such that the program determines whether the system is von Neumann or Harvard? Could there be another architecture or are these architectures the only ones known?
How can I tell whether my computer is Harvard or von Neumann architecture?
architecture;computer architecture
Your computer is a von Neumann machine.  All general purpose computers are.  The only exceptions are specialized co-processors like GPUs.  It's not that you can't have a Harvard machine (or any other architecture).  It's just that nobody builds them, especially not for sale (modulo co-processors, of course).