There are obvious examples that we've all heard before, such as Puff Daddy's "I'll Be Missing You" sampling The Police's "Every Breath You Take."
Or, Eminem sampling (one of my childhood favorites) Martika's "Toy Soldiers" in his song "Like Toy Soldiers."
One more example, this one from 1990... MC Hammer's "U Can't Touch This" sampling Rick James' "Super Freak."
Some artists choose to sample portions of the music, versus lyrics, such as Beastie Boys sampling AC/DC's "T.N.T." in "No Sleep Till Brooklyn."
Or probably one of the most famous, Vanilla Ice's "Ice Ice Baby" sampling Queen's "Under Pressure."
I will close with the following two quotes, as I think that they are right on target with designers appropriating images; learning from and paying homage to the artists who originally created certain pieces.
"Sampling's not a lazy man's way. We learn a lot from sampling, it's like school for us. When we sample a portion of a song and repeat it over and over we can better understand the matrix of the song." —Daddy-O of Stetsasonic, cited in Black Noise by Tricia Rose, Wesleyan Press 1994, p. 79
"When I sample something, it's because there's something ingenious about it. And if it isn't the group as a whole, it's that song. Or, even if it isn't the song as a whole, it's a genius moment, or an accident or something that makes it just utterly unique to the other trillions of hours of records that I've plowed through" —DJ Shadow, 33 1/3 Volume 24: DJ Shadow's Endtroducing..., 2005
Resources:images and samples from http://www.whosampled.com/