A clonoid is a set of finitary functions from a set A to a set B that is closed under taking minors. Hence clonoids are generalizations of clones. By a classical result of Post, there are only countably many clones on a 2-element set. In contrast to that, we present continuum many clonoids for A = B = {0, 1}. More generally, for any finite set A and any 2-element algebra B, we give the cardinality of the set of clonoids from A to B that are closed under the operations of B. Further, for any finite set A and finite idempotent algebra B without a cube term (with |A|, |B| ≥ 2) there are continuum many clonoids from A to B that are closed under the operations of B; if B has a cube term there are countably many such clonoids.