We consider a cell-free massive multiple-input multiple-output (MIMO) system with multiple antennas on the users and access points (APs). In previous works, the downlink spectral efficiency (SE) has been evaluated using the hardening bound that requires no downlink pilots. This approach works well for single-antenna users. In this paper, we show that much higher SEs can be achieved if downlink pilots are sent when having multi-antenna users. The reason is that the effective channel matrix does not harden. We propose a pilot-based downlink estimation scheme, derive a new SE expression, and show numerically that it yields substantially higher performance when having correlated Rayleigh fading channels. In cases with multi-antenna users, the APs can either coherently transmit the same data streams, or alternatively they transmit separate data streams non-coherently. The latter approach reduces the fronthaul signaling overhead, albeit with a potential SE penalty. For both strategies, we propose novel precoding and combining schemes. Specifically, we develop precoders based on the minimum mean square error (MMSE) criterion and investigate receive combining methods, including an MMSE combiner. Furthermore, we consider sharing different levels of channel knowledge between the APs. Finally, we present a comprehensive numerical analysis to validate our findings, evaluating the performance trade-offs associated with the number of users, APs, and antennas, as well as the choice of transmission strategy and the level of CSI sharing among APs.