The Decemberists are one band that springs to mind for telling great 'stories' in a song. The Island (off the Crane Wife, as well as the title track on that album) is divided into sections. And then there's The Mariner's Revenge Song on Picaresque. Guy who's been swallowed by a whale telling how he's spent his life seeking revenge on a man who ruined his family. Great stuff.

This thread could be extended to the ever-notorious 'concept album' too XD