Funny that people so often think of Bob Dylan and Leonard Cohen when listing "singers who can't sing." I've heard people say that about Willie Nelson too. But I hear that Joan Baez once (not too long ago) remarked about Dylan that one thing about him was "he can really sing!"   And when it comes to carrying a tune, I'd say that's true of Bob (or at least was during his first 3 decades of performing and recording), and it's also true of Willie. Leonard Cohen wasn't that good a singer in his early days, even if he had more range, but I love the sound of his later voice (the last 2 or 3 decades) -- not just his "storytelling," but the deep, gravelly sound of his low baritone.   

Now, Kristofferson is a different story. I've heard him go way off key or lose the tune in live performance, and I'd say he definitely is a much better songwriter and storyteller than singer.

Speaking of great songwriter/storytellers who can't sing all that well, how come nobody's mentioned Steve Earle?