Led Zeppelin
Led Zeppelin was one of the first heavy rock bands, and have been credited with shaping heavy metal music with the release of their sophomore album (Led Zeppelin II). From there, they went on to become one of the most successful rock bands in history, churning out nine albums and a great many rock classics (Communication Breakdown, Heartbreaker, Stairway to Heaven, etc.).
While Led Zeppelin has influenced many bands, such as Rush and Van Halen, they have made quite an impact on the gentlemen of Muse. Their song "Kashmir" was a huge inspiration for the bombastic drum and guitar combo found in Supremacy, and the band has played a couple of Led Zeppelin riffs; "Heartbreaker" was played at Glastonbury 2004, and "Whole Lotta Love" at Royal Albert Hall.
In addition, Jimmy Page, the guitarist for Led Zeppelin, came to see Muse perform at the iTunes Festival.