Joan Baez

Joan Baez, legendary folk singer from the 60s, best known for her amazing voice and activism.
According to some 80s tour rumor, the song "Hell in a Bucket" was penned after Joan said, of playing with the Grateful Dead, "I'd rather go to hell in a bucket." The rumor seems unlikely though, since Joan sat in with the Dead on five occasions, according to DeadBase, and shared the bill with them two other times. However, maybe it's something Joan said after she and Mickey Hart stopped dating?

I can't vouch for this story at all, but it's a good one all the same, taken from the description of a Joan Baez "Jackaroe" YouTube:

Joan says: I went to see Micky [sic] Hart when we wanted to get the Greateful [sic] Dead to do a Cambodian benefit with me.. that`s how I met him. All of his aquaintances [sic] are so slightly on the colorful wacky side. He was sitting with a blond guru with a dot and a turban when we were talking about the Cambodian refugees. After that , [sic]I was at home sitting at my desk writing my book when I looked out the window and saw Mickey in my front yard, banging on one of his esoteric drums and dancing around like a wild gnome. He could sense my isolation, even if he didn`t know me, and he was saying, "Hey you got to get out more." I began spending time with him and eventually we had the concept to collaborate on some recordings."

On to the Joan/GD collaborations throughout the years:

• According to DeadBase, the first time sit in is said to be for "Midnight Hour" on 7/16/66 at the Fillmore, along with Mimi "Farinalist"--could they mean Joan's daughter, Mimi Farina? However, the DeadBase setlist "may be incomplete" and indeed, the LMA has a few recordings for this show with different setlists, none of them containing "Midnight Hour."
• 3/23/75 at the Kezar found the boys on the same bill as Joan, but no sit-in. The show is still worth a listen, as it features Merl Saunders and Ned Lagin, no Donna, and the first "Blues for Allah" / "Stronger Than Dirt." It's a SNACK benefit show.
• 1/13/80 at the Oakland-Alameda County Coliseum ends with Joan singing. According to DeadBase, after the GD encore "U.S. Blues," Joan, the GD and the Beach Boys sing "Amazing Grace." According to the setlists on the LMA they sing "Bridging the Gap" (also known as "Land of a Thousand Dances"). According to the actual audio track names on the LMA, they sing "Land of a Thousand Dances" and "Amazing Grace." In "Land of Thousand Dances," mainly Joan is singing (and a bunch of people going "OH yeah!" and "Nah nah nah", someone is drumming, Phil is playing bass, Jerry is noodling (he gets a shout out for a brief solo from Joan). It's a Cambodian refugee benefit show.
• Throughout 1981, Mickey played in a historically unknown band High Noon, also featuring Bobby Vega and Merl Saunders. Joan sat in a number of times. A discussion of these shows can be found at Lost Live Dead
• 12/12/81 at Fiesta Hall in San Mateo features a Joan set, some of the boys sitting in, and a short Dead set. Dance for Disarmament benefit and the first "Me and Bobby McGee" since 10/16/74 (in Joan's set).
• 12/30/81 at the Oakland Auditorium Arena, features a mini set with Joan sans Brent (Brent is also missing for the second set opener, "Feel Like a Stranger"). 
• 12/31/81 still in Oakland, features another acoustic set with Joan, and this recording has four more tracks than what DeadBase lists (DeadBase, and most recordings, start at Me and Bobby McGee). Joan also comes out for "Must of Been the Roses" and "Aiko Aiko." "I don't know but I been told/ that a room with Deadheads is filled with soul yeah." Some Deadheads say this is the longest GD show ever, with four sets of music.
• 11/3/91 a tender memorial in Golden Gate Park for Bill Graham. Joan does not sit in, but is on the bill. Still check out this show, an amazing testament to Bill Graham, whose vision was essential to the Grateful Dead. The only GD "Forever Young" with Neil Young is especially tender, even if not the most musically smoking ever.
•  Since Jerry's passing, Joan has sat in with the remaining boys on different occasions. She sat in with Ratdog on 5/20/06, celebrating Wavy Gravy's 70th birthday at the Berkeley Community Theatre (I think it was the last of 20 Wavy birthdays celebrated in Berkeley). Humorously, Joan mistook the opening chords of Uncle John's Band as some folk song, "Little Darling, By the Diamonds." The look on everybody's face when she started singing...
• 4/20/08 (YouTube) features Mickey, Bobby, Joan, Michael Kang, Robin Slyvester, Tommy Lee Jones and a few others, on an oddly acoustic "Not Fade Away" in Speedway Meadows in Golden Gate Park. A Green Apple benefit. Ludacris (YouTube) persuading Mickey to let Tommy play...

The Rolling Stones

Garcia talking about Altamont, and by proxy, the Rolling Stones, in an 1981 Musician interview:

[Altamont was] an incredibly selfish scene. Steve
Gaskin pinned it down best when he said that Altamont was "the
little bit of sadism in your sex life the Rolling Stones had been
singing about all those years, brought to its most ugly, razor-
toothed extreme." Kind of ironic, since they were the ones who
started that "Sympathy For The Devil" stuff.

Outlaw Life

Jerry, on the Hell's Angels, in an 1981 Musician interview:

MUSICIAN: Can you talk about your relationship with the  Hell's
Angels? I played in a band backed by them in Berkeley  and it was,
uh...an ambivalent experience.
GARCIA: Well, that's it. It is ambivalent. I've always liked them 
because they don't hide what they are, and I think all they require of
you is honesty - they just require that you don't  bullshit them - and 
if you're out front with them, I think you  don't have anything to worry
about.
 The Angels are very conscious of their roots and history, so  the
fact that we played at Chocolate George's funeral way back during
the Haight-Ashbury was really significant to them. They didn't have
many friends in those days, and so anybody who would come out for
one of their members was demon strating true friendship. And with
them, that really counts for  something.
MUSICIAN: What do you feel attracted Kesey to them in the first
place? The noble savage concept?
GARCIA: No, I think Ken saw them for what they are: a definite
force of their own which you can't hope to control. When they
come around, it's reality, and you go with it.
MUSICIAN: What about Altamont?
GARCIA: Horrible.
MUSICIAN: It sure was. But having been in the Bay area at the time, I
can understand how you might have thought it a good idea to
recommend them as security people.
GARCIA: We didn't recommend them!!
MUSICIAN: I thought the Stones people said you suggested it?
GARCIA: Absolutely not!  No, we would never do that. The Angels
were planning on being there, and I guess the Stones crew thought
this might be a good way to deal with that fact.

The Who

Garcia, in an 1981 Musician interview:

I think the Who are one of the few truly 
important architects of rock 'n' roll. Pete Townshend may be 
one of rock 'n' roll's rare authentic geniuses. And there's also
the fact that they're among our few surviving contemporaries. . . 
I'm just really glad they exist. 

Pete Townsend and the GD "Not Fade Away" 3/28/81 in Essen, Germany
Jerry and Bobby doing windmills a la Townsend during "Truckin,'"4/12/78 Cameron Indoor (Duke University).
5/31/92 in Vegas, Bobby and Steve Miller doing windmills during Baba O'Riley. The GD played Baba O'Riley 12 times (sung by Vince), mainly in the Spring and Summer of '92 (first: 5/19/93; last: 11/29/94). With the exception of 11/29/94, it was always an Encore song, played into Tomorrow Never Knows (a Beatles song).

Hamza el Din and the Nubian Desert Trip

From a 1981 Musician article, Addendum #1:

"It's so great to meet someone who could be so damn strong and yet not
exude even a trace of evil, meaness, or  fear." A few years ago, Hart
accompanied Hamza on a journey  up the Nile to visit his ancestral
village in the Nubian Desert.  "The first thing those Nubian drummers
taught me was that Bo Diddley didn't invent that beat," said Mickey.
Not speaking Arabic, Hart utilized the universal language of music to 
exchange ideas and converse with the Sudanese, who were 
impressed with his dexterity. "Hamza had taught me to play the tar,
a single-membraned African drum, and his people were really blown
out by the rhythmic exercises I'd worked  up." The Nubians would
often hold the same rhythmic groove for hours, with different
sections of the ensemble coming forward to improvise over the
basic pattern. But when Hart's turn to solo came up he met with an
unexpected reaction from his hosts. "My polyrhythms startled them
at first. I asked  Hamza why they were staring at me, and he
explained that when they heard the off beat and polyrhythms they
felt I was forcing the drum. They feel the drums should tell you what
to  do, and not vice versa, which they see as artificial. They say, 
'Excite the drum and it will tell you what to play'," reflects Hart: 
"It's a great concept, and I've found it works if you approach the
instrument with the right attitude."

Airto Moreira

In a 1981 Musician interview, Hart talks about Airto:

"Airto gave me this Brazilian stringed instrument called the berimbau. He gave me a
quick lesson in how to play it, and I took it home to practice on.
Well, I wound up just staring into the fire  and playing this thing for
weeks. It just took over; I wouldn't accept phone calls or anything,"
laughs Hart. "Three weeks later I called up Airto and asked him what
the hell was going on!" and he explained that in Brazil the berimbau
was used to induce an altered state of consciousness for practicing
the  martial arts." Hart pauses. "The weird thing is that I've been
into the martial arts for years, but had let it go for a while, and 
then got back into it when I started playing the berimbau . . . And 
there was Airto talking about how this jungle instrument could take
you without you even knowing it!"

Francis Ford Coppola and Apocalypse Now

From Musician article in 1981, Addendum #1:

along with with bassist Phil Lesh, Airto, Flora Purim and others, accepted a
commission from Francis Ford Coppola to compose the score for Apocalypse Now: The Rhythm Devils Play River Music. 

Hart's marching orders from Coppola were short and to the point: "All
Francis said was 'you know what I want¿you know how to make
magic.  Do it!"' recalled  Hart. "I watched the film constantly. I had it
on video cassette in my kitchen, in my bedroom, and in the studio. It
played  continuously for three months." Their task was complicated 
by the fact that the battle sound effects Coppola brought back from
the Phillipines sounded unconvincing. In the end they were asked to
find a way of simulating the cacophony of war in the studio. "Try
reproducing the sounds of a napalm attack using wooden instruments
and bells;" suggests Hart wryly.  "The artillery sounded like cheap
firecrackers, so we had to reinforce that, too, with steel drums I
had built, and other  percussive devices. We had over fifteen hours of
material!"