Recently, there has been much interest in processing skyline queries for various applications that include decision making, personalized services, and search pruning. Skyline queries aim to prune a search space of large numbers of multi-dimensional data items to a small set of interesting items by eliminating items that are dominated by others. Existing skyline algorithms assume that all dimensions are available for all data items. This paper goes beyond this restrictive assumption as we address the more practical case of involving incomplete data items (i.e., data items missing values in some of their dimensions). In contrast to the case of complete data where the dominance relation is transitive, incomplete data suffer from non-transitive dominance relation which may lead to a cyclic dominance behavior. We first propose two algorithms, namely, "Replacement" and "Bucket" that use traditional skyline algorithms for incomplete data. Then, we propose the "ISkyline" algorithm that is designed specifically for the case of incomplete data. The "ISkyline" algorithm employs two optimization techniques, namely, virtual points and shadow skylines to tolerate cyclic dominance relations. Experimental evidence shows that the "ISkyline" algorithm significantly outperforms variations of traditional skyline algorithms.