How about Ensembl, with their genomic alignments? They've got multiple alignments (with a set of selected species e.g. for vertebrates you will have human, mouse, chicken; and pairwise alignment (human versus mouse, mouse versus fish, human versus fish, etc). This data can be seen on the browser (this is not the only option, just one example), retrieved through the Perl API or REST API.
Keep in mind that you won't have the alignment for all: they're difficulties with running the pipeline on fragmented assemblies of certain genomes. More information on their help page EPO Multiple Alignment.