Recent experiments on two-dimensional (2D) electron systems have found a sharp increase in the effective mass of electrons with decreasing electron density. In an effort to understand this behavior we employ the many-body theory to calculate the quasiparticle effective mass in 2D electron systems. Because the low density regime is explored in the experiments we use the GWγ approximation where the vertex correction γ describes the correlation effects to calculate the self-energy from which the effective mass is obtained. We find that the quasiparticle effective mass shows a sharp increase with decreasing electron density. Disorder effects due to charged impurity scattering plays a crucial role in density dependence of effective mass.