The Dead is famous for improvisational jamming, and their live concert tapes, most amateur are very popular.

In 1965 the bay area group which included Jerry Garcia, Phil Lesh on bass and Bill Kreutzmann on drums called themselves the Warlocks. Soon after they became the Grateful Dead.
They reached their height in the 70's, with the American Beauty and Workingman's Dead albums and the famous 1977 Cornell concert.
Garcia, however, was addicted to heroin by 1982, which resulted in his gradual decline as a guitarist. In 1995 Garcia was found dead in his room at a substance abuse treatment facility in Forest Knolls, California.

Bring Out Your Dead, NY Times April, 10, 2009:
The Grateful Dead was a 30-year ramble of touring. It continued after Garcia's death in a kind of post-history: first as the Other Ones, and later simply as the Dead (no "Grateful"), which is the name it will tour under this year. (The band now includes the original members Phil Lesh, Bob Weir, Mickey Hart and Bill Kreutzmann, as well as the guitarist Warren Haynes and the keyboardist Jeff Chimenti.

It was also an intellectual proposition, in how the band brought new information and states of mind to a century of American music: bluegrass, folk, blues, Motown, Bakersfield country and so on. For me it often works best intellectually; I confess I hear shortcomings even in a lot of good Dead shows - intonation problems, weak singing, calamitous rhythm.

Nearly 2,200 Dead shows exist on tape, of the 2,350 or so that the group played. Most of those are available online - either for free streaming on Web sites like archive.org and nugs.net, or for download on iTunes, like the "Dick's Picks" series and the more recent "Road Trips" archival series, which uses master-tape audio sources. DeadBase - Searchable Grateful Dead Setlists is another source.
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Deadheads have often been polled about their favorite show, through fanzines and Web sites. The answers have stayed fairly consistent. May 8, 1977, at Barton Hall, Cornell University.

Some consider a concert 20 days after Cornell, in Hartford just as good. (That show, taken from the master tapes engineered by Ms. Cantor-Jackson, has just been released by Rhino in heretofore unbeatable audio as "To Terrapin: Hartford '77.")

Because of the culture of taping and collecting around the concerts, the audience developed a kind of intellectual equity in the band. And as the fans traded more and more tapes. The pairing of Feb. 13 and 14, 1970, at the Fillmore East in New York - perhaps the first widely traded shows.

Also in 1987 the Dead had a hit single, "Touch of Grey." Suddenly the band was so popular that it could sell out Giants Stadium in July and return in September for a five-night run at Madison Square Garden.

Popular Songs:
Tennesee Jed, Jack Straw, Brown Eyed Woman, Sugar Magnolia and He's Gone.

Popular Albums:
American Beauty, Workingman's Dead
The triple disc, "Europe '72" is a collection of live sets.

Links:
dead.net/
FTP archive at Berkeley
Wikipedia
Classic Bands