There is more than one artist with this name:
1) Harem Scarem is a Rock band hailing from Ontario, Canada, formed in 1987 They renamed themselves Rubber in 1999 and released two albums under that name. In 2001, they went back to the Harem Scarem name. In the Summer of 2007 they announced they "will officially break-up after one more studio album."
2) Harem Scarem emerged from Melbourne's mid-80's indie scene, but, it could be argued, were closer in sound to classic Australian blues-rock from a decade before (Dingoes, Coloured Balls, Chain, Rose Tattoo etc.). Their sound was infused with a heady mix of punk spirit and Stax soul that also made them contemporaries of the likes of The Gun Club and the Beasts Of Bourbon.
Harem Scarem first appeared on the Melbourne Psychobilly compilation “Asleep at the Wheel”. They soon developed (via the “Dogman” EP and some key line-up changes) into a powerhouse live act, where Christopher Marshall's extraordinary, passionate vocals combined with Charlie Marshall's stonesy guitar.
With the classic line-up of the Marshall brothers, Barry Palmer (guitar), Glen Sheldon (bass), Peter Jones (drums) and Chris Wilson (harmonica & sax), the band went into the studio with producer John Archer (Hunters & Collectors) and emerged with this, their masterful 1986 album: Pilgrim's Progress (now re-issued by Aztec Music http://www.aztecmusic.net/)
3) Harem Scarem is a Scottish contemporary folk band http://www.haremscaremscotland.co.uk who have collaborated with Will Oldham AKA 'Bonnie Prince Billy'