Electrostatic screening in multilayer graphene is highly nonlinear due to the vanishing density of states at the Fermi level. Using a discrete model we study the charge screening normal to the layers. Our model shows a strong charge and temperature dependence and has a simple continuum limit at T=0 for undoped systems. Doped systems can exhibit more complex behavior due to minority-carrier screening. Most importantly we find that the screening length can vary more than an order of magnitude depending on the experimental conditions, reconciling the large range of screening lengths reported in previous experiments. This has important consequences for technological applications of multilayer graphene used in electrodes or transistor channels. © 2011 American Physical Society.