Call me bias, but out of all the instrumental versions of this song, I think it sounds most beautiful when played on a violin. There's something about the simplicity that only a single string melody can provide that seems to take people's breath away. Of course, this song was meant to be sung, and the words of John Newton are incredibly profound. However, when fresh out of vocalists, the violin is about as close to the human voice as one can get - but I'll save that for another day.
Here's my violin tutorial for "Amazing Grace". Enjoy!