Dave Grohl turned down drumming for Tom Petty and the Heartbreakers to eventually form the Foo Fighters:

“Following Cobain’s death in April 1994, Grohl retreated, unsure of where to go and what to do with himself. In October 1994, Grohl scheduled studio time, again at Robert Lang’s Studio, and quickly recorded a fifteen-track demo. With the exception of a single guitar part on “X-Static” played by Greg Dulli of the Afghan Whigs, Grohl performed all of the instruments himself.

At the same time, Grohl wondered if his future might be in drumming for other bands. In November, Grohl took a brief turn with Tom Petty and the Heartbreakers, including a memorable performance on Saturday Night Live. Petty asked him to join permanently, but Grohl realized that his future lay elsewhere, and thus he declined the invitation. Grohl’s name was also rumored as a possible replacement for Pearl Jam drummer Dave Abbruzzese, and Grohl even performed with the band for a song or two at three shows during Pearl Jam’s March 1995 Australian tour. However, by then, Pearl Jam had already settled on ex- Red Hot Chili Peppers drummer, Jack Irons, and Grohl had other solo plans in the works.”

(Source: Wikipedia)