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Understanding the concept of a Turing machine is actually quite important in real-world programming. A little digression -
Nearly everyone on this site will be able to point to an experience in their careers where they wrote something in Perl and it took them a couple days. Turned out to be really really useful and the PHB had it rewritten in Java. Took 15 people 6 months and it still doesn't work right.
Why is that? Perl isn't inherently a better language than Java. In fact, there are many things Java has better support for than Perl. However, Java projects generally take longer than the equivalent Perl projects and generally require more people.
My feeling is that Perl programmers tend to be more capable than Java programmers, precisely because we tend to have a stronger grasp of the fundamentals. Things like a Turing machine. In fact, I once implemented a Turing machine in production code because it was the correct and cost-effective solution to the requirements. It's easy to deride the theoreticals, but they're extremely useful, just not as presented. You actually have to think about how to apply them. :-p
My criteria for good software:
In reply to Re^3: Worst blog post ever on teaching programming