A neuromorphic chip that combines CMOS analog spiking neurons and memristive synapses offers a promising solution to brain-inspired computing, as it can provide massive neural network parallelism and density. Previous hybrid analog CMOS-memristor approaches required extensive CMOS circuitry for training, and thus eliminated most of the density advantages gained by the adoption of memristor synapses. Further, they used different waveforms for pre and post-synaptic spikes that added undesirable circuit overhead. Here we describe a hardware architecture that can feature a large number of memristor synapses to learn real-world patterns. We present a versatile CMOS neuron that combines integrate-and-fire behavior, drives passive memristors and implements competitive learning in a compact circuit module, and enables in-situ plasticity in the memristor synapses. We demonstrate handwritten-digits recognition using the proposed architecture using transistor-level circuit simulations. As the described neuromorphic architecture is homogeneous, it realizes a fundamental building block for large-scale energy-efficient brain-inspired silicon chips that could lead to next-generation cognitive computing.