Fascinating thread, as a non-singer myself, I received a great compliment at Shrewsbury FF by being told (by a very good Singer/Musician friend) that I will never have a great voice, but that I was a great singer (ie performer).
I only sing a couple of songs that I know back to front, but it's that knowledge and my will to get the songs across that comes through. You will never find a hostile session audience (unless you unleash a 107-verse mining disaster song on them :) ) as all sessions (esp at festivals) have such a range of abilities.
I only sing songs other people don't know (because I don't know the standard chorus songs myself) and I do panic if people start to join in as a musical accompaniment, but I concentrate on my perfomance of the song and let them worry about the rest.
Remember, it's the song you're trying to get across, and if you can convey the feeling and meaning of the song, well, in my book that's more than half way there, getting the bugger in tune, that's another thing.
Folks have already mentioned Dylan and Björk in this thread, I'd like to mention Leonard Cohen and Billy Bragg (early stuff in both cases) for where it's the song that counts. And in their words: "I was born with the gift of a golden voice" (LC: Tower of Song), and "There ain't nobody that can sing like me" (BB/Woody Guthrie: Way Over Yonder In a Minor Key)