We derive the Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts of random electromagnetic beams with arbitrary state and degree of polarization and spatial coherence. Further, we demonstrate the general formalism by calculating analytic expressions for the GH and IF shifts of an electromagnetic Gaussian Schell-model (EGSM) beam and show that the GH shifts may exist irrespective of the degree and state of polarization of the beam, while the IF shifts vanish when the beam is either s or p polarized or completely unpolarized. In addition, the spatial coherence width of the EGSM beam is found to influence only the angular GH and IF shifts.