I once compiled a playlist of covers of Don't Think Twice... there are so many! But none with the same poignancy. But I love Jerry Reed's cover (such a talented finger picker), it has a different emotional quality, but just as genuine IMHO.
Heh, I suppose I've just never been one to listen to many covers. I took a listen to that, though, and I agree; it's not quite the same emotionally, but it feels quite carefree and... funky.

It's an interesting change of pace!
Pink Floyd -
Mother