An alarming recent trend is seen in commercial music journalists, djs/vjs, etc. calling any music with a dj and mc "hip-hop." In doing this they obfuscate the distinction between rap and hip-hop. Rap is visceral; hip-hop is cerebral.
Rap has its own integrity, equal to that of hip-hop, as was shown in the old school (78 - 83) and Golden Age (84 - 93) years (all dates are approximations).
Rap is currently much more commercially successful and generally popular than hip-hop, and in its current expression has been watered down by the demands of commerce. (see: hip-pop). By contrast, hip-hop is undergoing a bit of a rennaisance, whose crystallisation was marked by the release of such albums Black Star by Mos Def and Talib Kweli in the late nineties.
Rap: Run DMC, Public Enemy, Eric B. and Rakim, Doug E. Fresh and Slick Rick, Beastie Boys, N.W.A./Dr. Dre, LL Cool J, Grandmaster Flash, BDP, Big Daddy Kane, Jay-Z, Black Thought (The Roots' mc), EPMD, Queen Latifah, MC Lyte, Kid and Play, Eminem, Snoop Dogg, Cash Money artists, Ludacris, Nelly, Black Eyed Peas (now?).
Hip-Hop: A Tribe Called Quest, De La Soul, Digital Underground, MF Doom, Aesop Rock, Mos Def, Talib Kweli, Del the Funky Homosapien, The Roots' musicians, Jurassic 5, 3rd Bass, Black Eyed Peas (then?), RJD2.
Some artists, such as Missy Elliot and Busta Rhymes, appear on first notice to be rappers, particularly because of their tendancy towards braggadoccio, etc., and thier somewhat accessible sound, but upon deeper examination prove to be hip-hop artists.
Similarly, The Neptunes, Timbaland, and Kanye West lay down what one might call hip-hop beats, but most often for rap artists.