We mechanically exfoliate mono- and few-layers of the transition metal dichalcogenides molybdenum disulfide, molybdenum diselenide, and tungsten diselenide. The exact number of layers is unambiguously determined by atomic force microscopy and high-resolution Raman spectroscopy. Strong photoluminescence emission is caused by the transition from an indirect band gap semiconductor of bulk material to a direct band gap semiconductor in atomically thin form.