The Perceptron algorithm, despite its simplicity, often performs well on online classification tasks. The Perceptron becomes especially effective when it is used in conjunction with kernels. However, a common difficulty encountered when implementing kernel-based online algorithms is the amount of memory required to store the online hypothesis, which may grow unboundedly. In this paper we present and analyze the Forgetron algorithm for kernel-based online learning on a fixed memory budget. To our knowledge, this is the first online learning algorithm which, on one hand, maintains a strict limit on the number of examples it stores and, on the other hand, entertains a relative mistake bound. In addition to the formal results, we also present experiments with real datasets which underscore the merits of our approach.