A biologically inspired approach to learning temporally correlated patterns from a spiking silicon retina is presented. Spikes are generated from the retina in response to relative changes in illumination at the pixel level and transmitted to a feed-forward spiking neural network. Neurons become sensitive to patterns of pixels with correlated activation times, in a fully unsupervised scheme. This is achieved using a special form of Spike-Timing-Dependent Plasticity which depresses synapses that did not recently contribute to the post-synaptic spike activation, regardless of their activation time. Competitive learning is implemented with lateral inhibition. When tested with real-life data, the system is able to extract complex and overlapping temporally correlated features such as car trajectories on a freeway, after only 10 min of traffic learning. Complete trajectories can be learned with a 98% detection rate using a second layer, still with unsupervised learning, and the system may be used as a car counter. The proposed neural network is extremely robust to noise and it can tolerate a high degree of synaptic and neuronal variability with little impact on performance. Such results show that a simple biologically inspired unsupervised learning scheme is capable of generating selectivity to complex meaningful events on the basis of relatively little sensory experience.