We discuss the finite versus infinite nature of C*-algebras arising from étale ample groupoids. For such a $G$, we relate infiniteness of the reduced groupoid C*-algebra $C^*_r(G)$ to notions of paradoxicality of a K-theoretic flavor. We construct a pre-ordered abelian monoid $S(G)$ which generalizes the type semigroup introduced by Rørdam and Sierakowski for totally disconnected discrete transformation groups. This monoid reflects the finite/infinite nature of $C^*_r(G)$ in the sense that if $G$ is minimal, principal, and $S(G)$ is almost unperforated, we obtain for $C^*_r(G)$ a dichotomy between the stably finite and purely infinite. Time permitting we will mention some applications for topological graph algebras as well as implications for continuous orbit equivalence of dynamical systems. This is joint work with Aidan Sims.