There is more than one artist with this name.

1) Mayflower is a punk band from Oswego, NY, United States.

Teddy Casper - guitar, vocals
Scott Gillard - guitar, vocals
Steve Port - drums
TJ Backer - bassmaster general
http://www.myspace.com/mayflower

2) Mayflower was an all-female rock band from Benevento, Italy, formed in 2006 and split up in 2008. A free EP can be downloaded at their offical website.

Miriam Mandato - vocals
Antonella Monetti - guitar
Laura Timoteo - bass
Daniela Pastore - drums
http://www.myspace.com/mayflowerspace

3) Mayflower is a from Seattle, WA, United States, expected to release a break-through LP in 2011.

Mercedes Silva - vocals, rhythm guitar
Alex Schumaker - lead guitar
Robert Domos - bass
Filip Pankovcin - drums

4) Mayflower was a post-apocalyptic rock group from Russia. After some years of active the band change it's name to Cafe Of Broken Dreams
http://www.last.fm/music/Cafe+Of+Broken+Dreams

Ilya Michaelsen - guitars, keyboards
K.K. Toch - drums and vocals