In addition to every album by "Weird Al" Yankovic, Bob Rivers puts his stuff online for free streaming here. He used to have all those songs available on albums, but now only a select few. There are some available for download, though. Then there are The Capitol Steps, who do political parodies. And there are countless others from whom I only have a few songs and no links.

EDIT: Tom Lehrer has about fifty songs, but I don't have a link for him. Just look for an album called, The Remains Of Tom Lehrer. It's every song he ever did and it should be relatively cheap.