We discuss the problem of ranking instances. In our framework, each instance is associated with a rank or a rating, which is an integer in 1 to k. Our goal is to find a rank-prediction rule that assigns each instance a rank that is as close as possible to the instance's true rank. We discuss a group of closely related online algorithms, analyze their performance in the mistake-bound model, and prove their correctness. We describe two sets of experiments, with synthetic data and with the Each Movie data set for collaborative filtering. In the experiments we performed, our algorithms outperform online algorithms for regression and classification applied to ranking.