An example of this kind of borrowing that I recognized myself was when Nirvana's "Come As You Are" first started getting airplay--I immediately thought that the main guitar riff sounded almost exactly like that in Killing Joke's "Eighties."
It's not clear which of these borrowings are intentional and which are accidental, but as English's book makes clear, this is an extremely common occurrence. Some of these have led to successful copyright infringement lawsuits, but most haven't--at least in the past. The Dr. Demento Show, which I used to listen to every week back in high school, used to have a regular feature called "Damaskas' Copycat Game" which would play short bits of songs in sequence, demonstrating their similarity.
Spider Robinson wrote a short story in 1983 called "Melancholy Elephants" which is a story about a woman who tries to persuade a Senator to oppose an extension of the term of copyright into perpetuity on the grounds that there are finite permutations of notes that are perceived as distinct musical melodies, and thus that the bill would result in an end to creation of new works. In the story, she succeeds in persuading him to kill the bill, while in reality, the equivalent bill--the Sonny Bono Copyright Term Extension Act of 1998--passed, and Larry Lessig and Eric Eldred failed to overturn it at the U.S. Supreme Court in 2003 (Eldred v. Ashcroft). While this didn't extend copyright to "in perpetuity," it has an economic effect virtually indistinguishable from copyright of infinite duration (as Justice Breyer's dissent recognized).
In 2005, arguments over the practice of sampling music came to a head, when the 6th Circuit Court of Appeals ruled that no sampling could take place without a license--not even for a 1.5-second, three-note guitar riff that N.W.A.'s 1990 song "100 Miles and Runnin'" sampled from Funkadelic's "Get Off Your Ass and Jam." This decision led to a protest in the form of a collection of songs composed solely of that sample. [The Downhill Battle organization's website has been down since November 2007, but can be found on the Internet Archive. -jjl, 6 Jan 2009.]
(Related: An excellent short video documentary about the use of a six-second drum sample from The Winstons' "Amen Brother.")
UPDATE (December 27, 2011): The Economist, Dec. 17-30, 2011 year-end issue features an excellent article, "Seven seconds of fire," about the Amen break.