Most folk music (as well as a lot of country) tends to have a story format rather than an "I love you" or "I hate you" repeated-ad-nauseum format...it's part of the reason why I listen to folk more than anything else. :) I'd list some for you, but my CDs are at home and my body is at work, and of course I can't remember anything off the top of my head. (A lot of Celtic music tends to be more story-teller-ish too, usually tragic stuff where everyone dies.)

(Ok, I'll give it a shot:

"The Thunder Rolls" and the one about the kid and the older woman where he was a ranch hand for her and she slept with him which I cannot remember what the name is, by Garth Brooks
"The Good Stuff" by Brad Paisley
"Red Rag Top" by Tim McGraw
"The Longest Road" by Stephen Fearing
"The Wreck of the Edmund FitzGerald" by Gordon Lightfoot
"Barrett's Privateers" and "Northwest Passage" by Stan Rogers

And apparently I can remember more than I think. :) )