It's true that a lot of the really good "three chord" songs actually have a change up or two, even if it's simple.

In "All the Small Things" by Blink 182, I used to think it was all three chords. After really listening to it, it turns out that in the chorus, another chord is created by some suspended notes in the vocals, and creating a V7 with a base note. In an interlude, the chords go I IV iii II. The change ups are pretty minor, but still serve to add interest.