  We compute leading order corrections to the entropy of any thermodynamic
system due to small statistical fluctuations around equilibrium. When applied
to black holes, these corrections are shown to be of the form $-k\ln(Area)$.
For BTZ black holes, $k=3/2$, as found earlier. We extend the result to anti-de
Sitter Schwarzschild and Reissner-Nordstrom black holes in arbitrary
dimensions. Finally we examine the role of conformal field theory in black hole
entropy and its corrections.
