We suggest two experimental methods for probing both short- and long-range spin correlations of atoms in optical lattices using superlattice potentials. The first method involves an adiabatic doubling of the periodicity of the underlying lattice to probe neighboring singlet (triplet) correlations for fermions (bosons) by the occupation of the resulting vibrational ground state. The second method utilizes a time-dependent superlattice potential to generate spin-dependent transport by any number of prescribed lattice sites, and probes correlations by the resulting number of doubly occupied sites. For experimentally relevant parameters, we demonstrate how both methods yield large signatures of antiferromagnetic correlations of strongly repulsive fermionic atoms in a single shot of the experiment. Lastly, we show how this method may also be applied to probe d-wave pairing, a possible ground-state candidate for the doped repulsive Hubbard model.