Upper limits for the electric charges on the atoms of cesium and potassium and the molecules of hydrogen and deuterium have been measured by a molecular beam deflection method. The results are: q(Cs)=(1.3+/-5.6)×10-17qe, q(K)=(-3.8+/-11.8)×10-17qe, |q(H2)|<2×10-15qe, and |q(D2)|<2.8×10-15qe (qe is the absolute value of the electron charge). They are consistent with the usual view that atoms and molecules are electrically neutral. The results on H2 and D2 provide very direct upper limits of 1×10-15qe for the electron-proton charge difference and 2.4×10-15qe for the neutron charge. The cesium result can be interpreted as showing that the magnitude of the electron charge differs from that of the proton by less than 5 parts in 1019 and that the neutron charge is less than 5×10-19qe. The relevance of charge equality to cosmological theory, and to the theory of elementary particles is discussed.