Associative learning of temporally disparate events is of fundamental importance for perceptual and cognitive functions. Previous studies of the neural mechanisms of such association have been mainly focused on individual neurons or synapses, often with an assumption that there is persistent neural firing activity that decays slowly. However, experimental evidence supporting such firing activity for associative learning is still inconclusive. Here we present a novel, alternative account of associative learning in the context of classical conditioning, demonstrating that it is an emergent property of a spatially extended, spiking neural circuit with spike-timing dependent plasticity and short term synaptic depression. We show that both the conditioned and unconditioned stimuli can be represented by spike sequences which are produced by wave patterns propagating through the network, and that the interactions of these sequences are timing-dependent. After training, the occurrence of the sequence encoding the conditioned stimulus (CS) naturally regenerates that encoding the unconditioned stimulus (US), therefore resulting in association between them. Such associative learning based on interactions of spike sequences can happen even when the timescale of their separation is significantly larger than that of individual neurons. In particular, our network model is able to account for the temporal contiguity property of classical conditioning, as observed in behavioral studies. We further show that this emergent associative learning in our network model is quite robust to noise perturbations. Our results therefore demonstrate that associative learning of temporally disparate events can happen in a distributed way at the level of neural circuits.