I think the Bar-Kays probably have the most amazing story of any band in history:

The Bar-Kays began in Memphis, Tennessee as a studio session musician group, backing major artists at Stax Records. They were chosen in 1967 by Otis Redding to play as his backing band. On December 10, 1967, Redding, his manager, and band members Jimmy King (b. 1949; guitar), Ronnie Caldwell (b. 1948; electric organ), Phalon Jones (b. 1949; saxophone), and Carl Cunningham (b. 1949; drums) died in a plane crash in Lake Monona while on their way to a performance in Madison, Wisconsin. 

Trumpeter Ben Cauley survived the crash and bassist James Alexander was on another plane, since there were eight members in Redding's party and the chartered plane could only hold seven. Cauley and Alexander rebuilt the group. The re-formed band consisted of Cauley; Alexander; Harvey Henderson, saxophone; Michael Toles, guitar; Ronnie Gorden, organ; Willie Hall, drums and later Larry Dodson, lead vocals. 

The group backed dozens of major Stax artists on recordings afterwards, including Isaac Hayes's Hot Buttered Soul. Cauley left the group in 1971, with Lloyd Smith joining in 1973 and the band changed musical direction in the during that decade to have a successful funk music career on Mercury Records. 

The Bar-Kays continued to have hits on R&B charts well into the 1980s. Marcus Price was also a member of the Bar-Kays, until he was murdered coming from rehearsal in 1984, a crime never solved by the Memphis police. The band took a hiatus in the late 1980s, but regrouped in 1991, with Alexander once again being the only original member involved. Alexander's son is the award-winning rapper and record producer, Phalon "Jazze Pha" Alexander, who was named after Phalon Jones.