  We apply the Asymptotic Iteration Method to obtain the bound-state energy
spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and
vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all
the exact solutions; when the potentials are both of Kratzer type, we obtain
all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions
under certain constraints on the potential parameters: in this case, a possible
general solution is found in terms of a monic polynomial, whose coefficients
form a set of elementary symmetric polynomials.
