I can't say that I am a big fan of rap/hip-hop, generally, but Public Enemy's It Takes a Nation of Millions to Hold us Back is still one of my favourite albums of all time.
Other favourites include Galaxie 500, Joy Division, My Bloody Valentine, Nick Cave and the Bad Seeds, The Velvet Underground, Billy Bragg, Bauhaus, Big Black, Dead Can Dance, The Prids, Mission of Burma, The The, Interpol, David Bowie, Talking Heads, The Smiths, Michael Franti, Massive Attack, Skinny Puppy, Fishbone, The Brian Jonestown Massacre, The Pogues, This Mortal Coil, The Pixies, The Clash, The Damned, Black Rebel Motorcycle Club, Tom Waits, The Decembrists, Thomas Dolby, Gary Numan, Atari Teenage Riot, Guided by Voices, Ministry, Ladytron, The Dresden Dolls, Psychic TV, Adam Ant, Orbital, Stereolab, Cocteau Twins, P.J. Harvey, 808 State, Belle & Sebastian, Public Images Ltd., Dead Kennedys, New Fast Automatic Daffodils, The Jesus and Mary Chain, The Orb, Sonic Youth, Aphex Twin, Spiritualized, Air, Phil Ochs, and most drum and bass.