Numerous experimental data suggest that simultaneously or sequentially activated assemblies of neurons play a key role in the storage and computational use of long-term memory in the brain. However, a model that elucidates how these memory traces could emerge through spike-timing-dependent plasticity (STDP) has been missing. We show here that stimulus-specific assemblies of neurons emerge automatically through STDP in a simple cortical microcircuit model. The model that we consider is a randomly connected network of well known microcircuit motifs: pyramidal cells with lateral inhibition. We show that the emergent assembly codes for repeatedly occurring spatiotemporal input patterns tend to fire in some loose, sequential manner that is reminiscent of experimentally observed stereotypical trajectories of network states. We also show that the emergent assembly codes add an important computational capability to standard models for online computations in cortical microcircuits: the capability to integrate information from long-term memory with information from novel spike inputs.