I'm not as much into the rap as into the hip hop, an indirect course I took by falling in love with trip hop, which makes up the most of my collection of 'beats' as it were. But, here's the list of bands I like that qualify:

Outkast, Gnarls Barkley, Dr Dre, Beastie Boys, Digable Planets, DJ Shadow, RJD2, Public Enemy, A Tribe Called Quest, Blackalicious, Ice-Cube, Ice-T, Run DMC, Disposable Heroes of Hiphoprisy, Gorillaz, MIA, Cee-Lo, Cut Chemist, Non Phixion, Sugarhill Gang, Coldcut, Loveage, Massive Attack, Mr Scruff, Nightmares on Wax, Portishead, Propellerheads, Sneaker Pimps, Thievery Corporation, UNKLE, and probably more that I haven't thought of.