Thanks for the comments everyone! I'm pretty familiar with the Dead's non-Dead folky stuff: the albums Garcia made with David Grisman are all excellent. I got to see them play a couple of times at the Warfield theater in SF, they should release a live recording of one of those show, it was great! And the Dead have officially released a CD of their jug band incarnation "Mother McCree's Uptown Jug Champions" which is also lots of fun. They cover wierd old tunes like "Boodle Am Shake," "Beedle Um Bum," "Cocaine Habit Blues" (sadly appropriate), and "In the Jailhouse Now." I highly recommend it.
The songs that are turning up from this survey are generally the ones that I was suspecting would turn up, with the possible exception of Catfish John. I think that several of you make very good points that A) often Dead songs have decptively tricky chord progressions. The songs sound easy, but once you get in there it can be hard to find the right chord. and B) the rhythmic complexity of the Dead's music is hard to replicate with a single acoustic guitar.
What about the Dead's songs "Fire on the Mountain," or "Franklin's Tower" (that's the one with the chorus "Roll away the dew..."). Has anyone heard either of those tunes at folk circles?