A comprehensive experimental study of the dynamics and rheology of concentrated aqueous dispersions of poly(ethylene glycol)-grafted colloidal spheres is reported. The study focuses on good solvent conditions, for which excluded-volume interactions dominate. At high concentrations a glass transition is evident from the nondecaying component of the intensity correlation function measured with three-dimensional dynamic light scattering. Results for the linear viscoelastic and steady shear rheology on approaching the glass transition correlate well with the slowing of the diffusive dynamics; in particular, at, or close to, the concentration where the dynamics becomes nonergodic, the dispersions acquire a low-frequency plateau in the elastic shear modulus as well as a yield stress. The overall behavior of the dispersions conforms to that of hard-sphere dispersions; however, some qualitative differences are observed in the evolution of the dynamics and rheology with increasing concentration near the glass transition.