This paper considers multi-cell massive multiple-input multiple-output systems, where the channels are spatially correlated Rician fading. The channel model is composed of a deterministic line-of-sight path and a stochastic non-line-of-sight component describing a practical spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE), element-wise MMSE, and least-square channel estimates for this model. Using these estimates for maximum ratio combining and precoding, rigorous closed-form uplink (UL) and downlink (DL) achievable spectral efficiency (SE) expressions are derived and analyzed. The asymptotic SE behavior, when using the different channel estimators, are also analyzed. The numerical results show that the SE is higher when using the MMSE estimator than that of the other estimators, and the performance gap increases with the number of antennas.