In this paper, we present an alternative approach to neuromorphic systems based on multi-level resistive memory (RRAM) synapses and deterministic learning rules. We demonstrate an original methodology to use conductive-bridge RAM (CBRAM) devices as, easy to program and low-power, binary synapses with stochastic learning rules. New circuit architecture, programming strategy and probabilistic STDP learning rule for two different CBRAM configurations 'with-selector (1T-1R)' and 'without-selector (1R)' are proposed. We show two methods (intrinsic and extrinsic) for implementing probabilistic STDP rules. Fully unsupervised learning with binary synapses is illustrated with the help of two example applications: (i) real-time auditory pattern extraction (inspired from a 64-channel silicon cochlea emulator) and (ii) visual pattern extraction (inspired from the processing inside visual cortex). High accuracy (audio pattern sensitivity>2, video detection rate>95%) and low synaptic-power dissipation (audio 0.55µW, video 74.2µW) are shown. The robustness and impact of synaptic parameter variability on system performance is also analyzed.