We present practical parallel algorithms using prefix computations for various problems that arise in pairwise comparison of biological sequences. We consider both constant and affine gap penalty functions, full-sequence and subsequence matching, and space-saving algorithms. Commonly used sequential algorithms solve the sequence comparison problems in O(mn) time and O(m+n) space, where m and n are the lengths of the sequences being compared. All the algorithms presented in this paper are time optimal with respect to the sequential algorithms and can use processors where n is the length of the larger sequence. While optimal parallel algorithms for many of these problems are known, we use a simple framework and demonstrate how these problems can be solved systematically using repeated parallel prefix operations. We also present a space-saving algorithm that uses space and runs in optimal time where p is the number of the processors used. We implemented the parallel space-saving algorithm and provide experimental results on an IBM SP-2 and a Pentium cluster.