We study the temperature (T) dependence of magnetic penetration depth λ(T) from microwave surface impedance measurements in single crystals of Bi 2 Sr 2 CaCu 2 O 8 + y with various oxygen contents. At relatively low oxygen content, both the in-plane (λ a b ( T ) and out-of-plane (λ c (T)) penetration depths show the T-linear behavior at low temperatures, consistent with a clean d-wave superconductor. In contrast, overdoped samples exhibit T 2 dependence of λ a b (T) and λ c (T). This strongly suggests that the quasiparticle excitation spectrum changes into that of a gapless state with oxygen doping.