I don't really listen to bands. I mostly listen to artists. I guess one of my favorite bands would be Fun., them and the Beatles, but those are really the only bands I listen to.
I have a ton of favorite artists though, but the ones I listen to most frequently would be:
Joanna Newsom
Soko
Bob Marley
Joan Baez
Bob Dylan
Donovan and
David Bowie

My current favorite song is "Moonage Daydream" by Bowie.