This is probably more of an example than a counterexample. Consider the following binary operation table defined on a three element set with zero:
0 1 2 0 0 0 0 1 0 0 1 2 0 2 2V. Murskii showed that the equational theory of this algebra has no logically equivalent (in equational logic) finite theory. Lyndon earlier showed that every two element algebra with one binary operation did have a finite basis, and Perkins found a six element semigroup with no finite basis. I don't know the status of algebras with a single ternary operation.
Gerhard "Ask Me About System Design" Paseman, 2010.06.21