Negative examples - genes that are known not to carry out a given protein function - are rarely recorded in genome and proteome annotation databases, such as the Gene Ontology database. Negative examples are required, however, for several of the most powerful machine learning methods for integrative protein function prediction. Most protein function prediction efforts have relied on a variety of heuristics for the choice of negative examples. Determining the accuracy of methods for negative example prediction is itself a non-trivial task, given that the Open World Assumption as applied to gene annotations rules out many traditional validation metrics. We present a rigorous comparison of these heuristics, utilizing a temporal holdout, and a novel evaluation strategy for negative examples. We add to this comparison several algorithms adapted from Positive-Unlabeled learning scenarios in text-classification, which are the current state of the art methods for generating negative examples in low-density annotation contexts. Lastly, we present two novel algorithms of our own construction, one based on empirical conditional probability, and the other using topic modeling applied to genes and annotations. We demonstrate that our algorithms achieve significantly fewer incorrect negative example predictions than the current state of the art, using multiple benchmarks covering multiple organisms. Our methods may be applied to generate negative examples for any type of method that deals with protein function, and to this end we provide a database of negative examples in several well-studied organisms, for general use (The NoGO database, available at: bonneaulab.bio.nyu.edu/nogo.html).