We investigate sl(n) conformal Toda theory with maximally symmetric boundaries, using classical and conformal bootstrap methods. We compare the results with the well-known case of Liouville theory (n = 2). For all values of n >= 2, we find that there exist D-branes of all possible dimensions 0 <= d <= n-1. For n >= 3 however, there appear infinite multiplicities in the boundary spectrum, in sharp contrast with the Liouville case.