Diatomic potentials for krypton are computed and also probed experimentally. For a probe-laser wavelength near 811 nm, several strong dipole-dipole interactions produce purely-long-range potential wells in the singly excited manifold of (s+p) potentials and in the doubly excited manifold of (p+p) and (s+d) potentials. Evidence of resonant photoassociation into bound states of these potential wells is observed in the emission of ions and ultraviolet photons from a magneto-optically trapped krypton cloud.