Tindersticks. Tindersticks - Tiny Tears - YouTube
But I think the sound is purposeful, and I happen to love it. Honestly I think even autotune would struggle with this music… 
And I came here to nominate Liz Phair. That woman just plain old cannot sing.
Her stuff gets cleaner later on, but it also loses its charm, in my opinion. I just love her voice on Exile.
Completely agree. Her voice in her first few albums, in particular Exile, just sounds so earnest and personal.
What you got against Colin? Did he attack you with a raspberry???
Really? That’s one of my favorite songs on one of my favorite albums. Love the growly way she sings it. Now, I have absolutely no musical ability, can’t keep a pitch or a beat (no, seriously, I’ve actually been tested), so maybe I just can’t recognize that’s she’s out of tune. But I love that song.
Shaun Ryder of the Happy Mondays. Their stuff was just supposed to be trippy, druggy dance music. And maybe the intended melodies weren’t conventional to begin with. But, boy, his “singing” was just all over the map.
Joni Mitchell. Her lower register is just fine, but she like to sing a lot in the octave above that and it’s awful. Too bad… great artist otherwise.
I’m not entirely sure auto-tune would have helped with Shaun Ryder. I like his vocal stylings – they’re very distinct – but I can see why people don’t glom to it – it ain’t the pitch, so far as I can tell. It’s the timbre and phrasing and other quirks with it, which auto-tune ain’t gonna help.