We introduce simple practical approximations for various diffusion-influenced reactions in two dimensions, which are found to be superior to previously known approximations at long times. The approximations for the irreversible reactions with the Smoluchowski boundary condition are found to be in excellent agreement with the numerically exact results at all times. We generalize the long-time approximations to be applied to more complicated geminate diffusion-reaction systems such as the excited-state reversible binding and transfer reactions. (C) 2011 Elsevier B.V. All rights reserved.