Spatial nonlocality in the optical response of noble metals is shown to produce significant blue shift and near-field quenching of plasmons in nanoparticle dimers, nanoshells, and thin metal waveguides. Compared with a local description relying on the use of frequency-dependent dielectric functions, we predict resonance shifts as large as 10% and field-intensity reduction of an order of magnitude at interparticle distances or metal thicknesses below 2 Å, although sizable effects are already observed for dimers separated by 2 nm. The calculation method (a combination of the specular-reflection model and a suitable nonlocal extension of measured local dielectric functions) is simple to implement and can be easily generalized to arbitrarily complex nanostructures.