Nurses and other health researchers are often concerned with infrequently occurring, repeatable, health-related events such as number of hospitalizations, pregnancies, or visits to a health care provider. Reports on the occurrence of such discrete events take the form of non-negative integer or count data. Because the counts of infrequently occurring events tend to be non-normally distributed and highly positively skewed, the use of ordinary least squares (OLS) regression with non-transformed data has several shortcomings. Techniques such as Poisson regression and negative binomial regression may provide more appropriate alternatives for analyzing these data. The purpose of this article is to compare and contrast the use of these three methods for the analysis of infrequently occurring count data. The strengths, limitations, and special considerations of each approach are discussed. Data from the National Longitudinal Survey of Adolescent Health (AddHealth) are used for illustrative purposes. © 2005 Wiley Periodicals, Inc. Res Nurs Health 28: 408–418, 2005.