Layered MAX phases are exfoliated into 2D single layers and multilayers, so-called MXenes. Using first-principles calculations, the formation and electronic properties of various MXene systems, M2C (M = Sc, Ti, V, Cr, Zr, Nb, Ta) and M2N (M = Ti, Cr, Zr) with surfaces chemically functionalized by F, OH, and O groups, are examined. Upon appropriate surface functionalization, Sc2C, Ti2C, Zr2C, and Hf2C MXenes are expected to become semiconductors. It is also derived theoretically that functionalized Cr2C and Cr2N MXenes are magnetic. Thermoelectric calculations based on the Boltzmann theory imply that semiconducting MXenes attain very large Seebeck coefficients at low temperatures.