Results are presented from a search for particle dark matter (DM), extra dimensions, and unparticles using events containing a jet and an imbalance in transverse momentum. The data were collected by the CMS detector in proton-proton collisions at the LHC and correspond to an integrated luminosity of 19.7 fb-1 at a centre-of-mass energy of 8 TeV. The number of observed events is found to be consistent with the standard model prediction. Limits are placed on the DM-nucleon scattering cross section as a function of the DM particle mass for spin-dependent and spin-independent interactions. Limits are also placed on the scale parameter MD in the Arkani-Hamed, Dimopoulos, and Dvali (ADD) model of large extra dimensions, and on the unparticle model parameter ΛU. The constraints on ADD models and unparticles are the most stringent limits in this channel and those on the DM-nucleon scattering cross section are an improvement over previous collider results.