Interesting results in TCS which are easily explainable to programmers without technical background
In addition to the halting problem, I suggest discussing:

Rice's Theorem.  Some of the explanation on Wikipedia is a bit jargon-heavy, but it's generally not a hard theorem or proof to understand other than that; it has a lot of relevance to real-world concepts like anti-virus software.  The proof is about as involved as the proof of the halting problem (and actually depends on the undecidability of the halting problem).  Basically, just understand that a "computable function" is a Turing machine or computer program.