In exercise 1.2.11. of Bump's Automorphic Forms and Representations book, he deals with real quadratic fields $K$ in which $\mathcal{O}_K$ is generated (as a ring) by its norm-1 units. In this case one get a nice relationship between ideal classes and hyperbolic conjugacy classes. However, as Bump comments, this condition is not always satisfied (for real quadratic fields).

So my question is: for what number fields $K$ is $\mathcal{O}_K$ generated by the norm-1 units? Moreover, does being so generated have analogous implications for $K$ or its ideal class group?

Some obvious observations: it basically never happens for imaginary quadratic $K$, it always happens for cyclotomic $K$, and (I believe) it's pretty rare for real quadratic $K$.

Other observations and examples, obvious or not, are welcome in lieu of a complete answer.