Once you compile a program using standard libraries, the program should run on all versions of the OS it was compiled under (if you have Windows, it should run on all versions of Windows, etc.). I'm not 100% sure as to what DLLs you might need to run the program, but it really depends on what you put into your code. Some features of C++ may require a DLL depending on how your compiler implemented it.
As far as I know, DEV-C++ doesn't require any DLLs for basic applications and as long as you stuck with C++ standards, you should be able to run it on any other computer as long as they have the same OS.
Why not compile the code to a stand-alone .exe and then let it run. That is assuming the same OS. Dev C++ is only for code creation and editing, it is not required once you have compiled and built the program.