  Kaplansky introduced the notions of CCR and GCR $C^*$-algebras because they
have a tractable representation theory. Many years later, he introduced the
notions of CCR and GCR rings. In this paper we characterize when the algebra of
an ample groupoid over a field is CCR and GCR. The results turn out to be exact
analogues of the corresponding characterization of locally compact groupoids
with CCR and GCR $C^*$-algebras. As a consequence, we classify the CCR and GCR
Leavitt path algebras.
