Data collection is usually performed in wireless sensor networks by the sensors relaying data towards a static control center (sink). Motivated by important applications (mostly related to ambient intelligence and remote monitoring) and as a first step towards introducing mobility, we propose the basic idea of having a sink moving in the network area and collecting data from sensors. We propose four characteristic mobility patterns for the sink along with different data collection strategies. Through a detailed simulation study, we evaluate several important performance properties of each approach. Our findings demonstrate that by taking advantage of the sink's mobility and shifting work from sensors to the powerful sink, we can significantly reduce the energy spent in relaying traffic and thus greatly extend the lifetime of the network.