Influential?
Beatles, of course....seconded.
Nice on the Bill Haley....also seconded.
Bob Marley
Black Sabbath
Nirvana
Miles Davis
Herbie Hancock
Prince and the Revolution (Read: Just The artist formerly Known as 'the Artist Formerly Known as Prince')
Beastie Boys
Ray Charles
Marvin Gaye
The Beach Boys....(seriously.)
David Bowie
James Brown
Aretha Franklin
Otis Redding
Mary J. Blige
Sid Vicious/Sexpistols
Augustus Pablo
The Who
Just to name a few.....

Personally, the one group that changed the way I thought of music was 'Sublime.'
http://en.wikipedia.org/wiki/Sublime_%28band%29If you've never heard them, or only heard 'What I Got,' 'Santeria,' or 'Wrong Way,' you should really give them a listen.
They have tons of great music even though Brad overdosed before they ever had the chance to get huge.
If he hadn't, I believe they would have been one of the most legendary bands of all-time.
~archi