Bioinformatics researchers need efficient means to process large collections of genomic sequence data. One application of interest, genome assembly, has great potential for parallelization; however, most previous attempts at parallelization require uncommon high-end hardware. This paper introduces the Scalable Assembler at Notre Dame (SAND) framework that can achieve significant speedup using large numbers of commodity machines harnessed from clusters, clouds, and grids. SAND interfaces with the Celera open-source assembly toolkit, replacing two independent sequential modules with scalable parallel alternatives: the candidate selector exploits distributed memory capacity, and the sequence aligner exploits distributed computing capacity. For large problems, these modules provide robust task and data management while also achieving speedup with high efficiency. We show results for several data sets ranging from 738 thousand to over 320 million alignments using resources ranging from a small cluster to more than a thousand nodes spanning three institutions.