Corollaries of the Yoneda Lemma in Analysis?
The underlying idea is extremely important in analysis; a simple example is that you can embed any inner product space into the space of linear functionals on its conjugate by the linear transformation $v \mapsto \langle -, v\rangle$.
It's not an application of Yoneda lemma, but it's clearly the same sort of idea. In fact, there's a good analogy between inner products and hom-set functors, which can sometimes be used to translate ideas back and forth.