  The entropy for two-dimensional black holes is obtained through the entropy
function with the condition that the geometry approaches an $AdS_2$ spacetime
in the near horizon limit. It is shown that the entropy is universal and
proportional to the value of the dilaton field at the event horizon as
expected. We find this universal behavior holds even after the inclusion of
higher derivative terms, only modifying the proportional constant. More
specifically, a variety of models of the dilaton gravity in two dimensions are
considered, in which it is shown that the universal entropy coincides with the
well-known results in the previous literatures.
