Tom Lehrer's album, That Was The Year That Was, was pretty much entirely topical songs.

The (Chad) Mitchell Trio did a few songs not yet listed in this thread; Barry's Boys, The I Was Not A Nazi Polka, The Ecumenical March, one about Lurleen Wallace (It's great that you're governor, Lurleen...), Which Hat Shall I Wear, a parody version of The Twelve Days Of Christmas, and many more.