Coming up with "The" one thing a programmer should know seems too narrow a question. Kind of like "What is your favorite song?" instead of "What are some of your favorite songs?" A more interesting question might be "What things would you emphasize to someone learning to program?" Flexibility? Precision? My answer:

Every programmer should

1. Learn C / Assembly - Understand how code interacts with hardware.

2. Learn Lisp - Understand how ideas interact with code (and vice versa).

3. Learn "O" notation - Understand algorithm complexity.

4. Be clean and flexible.