Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.