Dielectric fluctuations are shown to be the dominant source of noncontact friction in high-sensitivity scanning probe microscopy of dielectric materials. Recent measurements have directly determined the friction acting on custom-fabricated single-crystal silicon cantilevers whose capacitively charged tips are located 3-200 nm above thin films of poly(methyl methacrylate), poly(vinyl acetate), and polystyrene. Differences in measured friction among these polymers are explained here by relating electric field fluctuations at the cantilever tip to dielectric relaxation of the polymer.