Due to the advent of high-throughput microarray technology, it has become possible to develop molecular classification systems for various types of cancer. In this article, we propose a new methodology using regularized regression models for the classification of tumors in microarray experiments. The performance of principal components, partial least squares and ridge regression models is studied; these regression procedures are adapted to the classification setting using an optimal scoring algorithm. We also develop a procedure for ranking genes based on the fitted regression models. The proposed methodologies are applied to two microarray studies in cancer.