Off the top of my head, there are many Townes Van Zandt covers that are really great (Steve Earle – Rex’s Blues and Tecumseh Valley, Guy Clark-No Lonesome Tune and REK – Snowin on Raton, Norah Jones – Be here to Love Me, to name a few).
Cross Canadian Ragweed does a good job with Neil Young’s The Needle and the Damage done.
I love Patty Griffin, but I prefer Bruce’s version. I guess maybe I don’t “buy” into that song when sung by a female.