We investigate the synchronization transitions in systems of coupled oscillators. Based on the Ott-Antonsen reduction for phase oscillators with sinusoidal coupling, we analyze the stability of incoherent and partially synchronized states. Using this method, we show that in globally coupled systems with certain unimodal frequency distributions, there appear unusual types of synchrony transitions, where synchrony can decay with increasing coupling, incoherence can regain stability for increasing coupling, or multistability between partially synchronized states and/or the incoherent state can appear. In one-dimensional arrays of oscillators with non-local coupling one can observe at the onset of synchrony the emergence of collective macroscopic chaos as an intermediate stage between complete incoherence and stable partially coherent plane waves. In both cases, the phase lag in the interaction function plays an important role for the observed phenomena.