God I love this song. It's been a favorite of mine lately, especially the late-70s to early 80s versions. It's got to be one of the most beautiful songs they ever played, and on certain nights, it could touch even the toughest of souls.
The Dead's version was based upon a old, traditional folk song of Scottish origin. The original song eventually took a new life in the Southern United States. Dylan had a similar version on his debut album in '62 called "Pretty Peggy-O". The Dead first played it in December of 73, where it remained a staple for the next 22 years.
It starts off with a rolling Jerry-riff, then the rest of the band just kinds of folds into a slow, smooth shuffle. Jerry kicks in and takes you on a journey with Peggy and her sweet William. What can really make this song special though is Jerry's solo. Done right, it can soar to amazing, emotional heights.
I've been listening to alot of 1977 lately, a particularly good year for this song. A truly excellent version can be found during the 5/5/77 show. Check it out.