I'd nominate the standard high school + college math curriculum (algebra and geometry up through the first two semesters of college calculus; multivariable calculus and differential equations are less general). It forms the basis for a lot of science and engineering; one way you know that you really understand something is when you can reduce it to math.
So, transferable skills: skills that, upon improvement, increase your ability in other areas (and also improve other, higher-level skills).
A basic example would be reading/writing. Knowing how to read and write allows one to access a huge amount of other skills and resources which are otherwise unavailable. A less obvious example would be clear speech (enunciation). Ability to speak clearly improves one's prospects in a lot of different areas (e.g. professional advancement, dating, etc.).
I'm looking for additional examples. Which skills did you find to be most transferable? Did you become proficient in X, and then found this helped you in many other areas of your life? Please share.
(I tried to find whether this was discussed before, and failed; if it was, I would appreciate the link.)