At the very least, proving that a game is Turing complete can be as entertaining a challenge as playing it. One case where Turing completeness was useful was i

At the very least, proving that a game is Turing complete can be as entertaining a challenge as playing it. One case where Turing completeness was useful was in proving wrong those programmers who claimed that there were some programs that just could not be written using structured programming. Also, if we did not know about Turing completeness, there would be constant futile research trying to find alternative architectures and languages that could solve problems that cannot be solved with what we have.