High-resolution array comparative genomic hybridization (aCGH) provides exon-level mapping of DNA aberrations in cells or tissues. Such aberrations are central to carcinogenesis and, in many cases, central to targeted therapy of the cancers. Some of the aberrations are sporadic, one-of-a-kind changes in particular tumor samples; others occur frequently and reflect common themes in cancer biology that have interpretable, causal ramifications. Hence, the difficult task of identifying and mapping common, overlapping genomic aberrations (including amplifications and deletions) across a sample set is an important one; it can provide insight for the discovery of oncogenes, tumor suppressors, and the mechanisms by which they drive cancer development. In this paper we present an efficient computational framework for identification and statistical characterization of genomic aberrations that are common to multiple cancer samples in a CGH data set. We present and compare three different algorithmic approaches within the context of that framework. Finally, we apply our methods to two datasets - a collection of 20 breast cancer samples and a panel of 60 diverse human tumor cell lines (the NCI-60). Those analyses identified both known and novel common aberrations containing cancer-related genes. The potential impact of the analytical methods is well demonstrated by new insights into the patterns of deletion of CDKN2A (p16), a tumor suppressor gene crucial for the genesis of many types of cancer.