Must we restrict ourselves to bands? I always wonder at what point it became fashionable to talk of all musical acts as bands. Virtually all of my favorite artists are solo acts that will sometimes play with backup musicians - hardly bands, though.
In any case, my favorite song is "Thirsty Boots," written by Eric Andersen in response to the 1964 Freedom Summer voter registration drives in the segregated South. Eric does not have a voice, though, so my favorite rendition of it is John Denver's.
My other favorite songs include "A Man's a Man for a'That," a song written by the Scottish poet Robert Burns in 1795, and "The Mary Ellen Carter" by Stan Rogers.