Indirect excitons in coupled quantum wells are long-living quasiparticles, explored in the studies of collective quantum states. We demonstrate that, despite the extremely low oscillator strength, their spin and population dynamics can by addressed by time-resolved pump-probe spectroscopy. Our experiments make it possible to unravel and compare spin dynamics of direct excitons, indirect excitons, and residual free electrons in coupled quantum wells. Measured spin relaxation time of indirect excitons exceeds not only one of direct excitons but also one of free electrons by two orders of magnitude.