  We report the temperature T and oxygen concentration dependences of the
penetration depth of grain-aligned YBa_2Cu_3O_{7-\delta} with \delta= 0.0, 0.3
and 0.43. The values of the in-plane \lambda_{ab}(0) and out-of-plane
\lambda_{c}(0) penetration depths, the low temperature linear term in
\lambda_{ab}(T), and the ratio \lambda_{c}(0) /\lambda_{ab}(T) were found to
increase with increasing $\delta$. The systematic changes of the linear term in
\lambda_{ab}(T) with T_c found here and in recent work on HgBa_2Ca_{n-1}
Cu_nO_{2n+2+\delta} (n = 1 and 3) are discussed.
