Measurement of coupled quantum systems plays a central role in quantum information processing. We have realized independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is all-electrical, cross-talk between the two measurements is negligible, and read-out fidelities are ∼86% on average. This allows us to directly probe the anticorrelations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. The results provide a possible route to the realization and efficient characterization of multiqubit quantum circuits based on single quantum dot spins.