There are 2 bands called Consequence

1. A Rapper from New York
2. An Electro project from Germany

1.Consequence (born Dexter Raymond Mills, Jr.) is an American hip hop artist from Queens, NY, he is most notable for appearing frequently on A Tribe Called Quest's Beats, Rhymes and Life, and has recently re-emerged on a series of tracks with Kanye West, as well as featuring on the song "Spaceship" off West's The College Dropout, and the song "Gone" off West's second album Late Registration. He is currently signed to Kanye West's GOOD Music record label. He is also the cousin of A Tribe Called Quest's Q-Tip.

Discography (Rapper) at Discogs:
http://www.discogs.com/artist/Consequence+(2)

2.ConseQuencE! is an EBM / Electro project from Germany. They released on different labels in the USA, Germany. The band was formed in 1985. The style changed from hard industrial electro/EBM (80s-90s) to synthpop (Mid 95-2000) and ambient after 2001.

Official Site:
http://www.consequence.info

Discography (Electro Project) at Discogs:
http://www.discogs.com/artist/Consequence

More Info:
http://www.answers.com/topic/consequence-rapper?cat=entertainment
http://www.artistdirect.com/nad/music/artist/card/0,,563229,00.html?src=search&artist=Consequence
http://www.rollingstone.com/artists/consequence/albums/album/321406/volition