When it comes to attribution I like to avoid such ugly terms as plagiarism, stealing, and blatant rip-off. Instead, I say that a song reminds me of another, or that a writer may have been influenced by somebody else's work. Perhaps they subconsciously borrowed, or they believed that an old melody was in the public domain anyway. I mean, who needs email from angry songwriters?
Will Shade, over at the music webzine Perfect Sound Forever, has no such qualms. He comes down hard on Jimmy Page for his role in the uncredited recycling of material, first by the later-period Yardbirds and then by Led Zeppelin. The article's title is unambiguous: The Thieving Magpie: Jimmy Page's Dubious Recording Legacy. In one or two cases, the claims have been pursued successfully in the courts, notably by Willie Dixon, who wrote the Muddy Waters song You Need Love (1962), the ultimate source of Led Zeppelin's Whole Lotta Love (1969), via the Small Faces' You Need Loving (1966).
Will Shade discusses a long list of Yardbirds and Led Zeppelin songs and their uncredited sources, mainly from blues artists. I hate to disillusion you completely, but not even Stairway To Heaven comes out of it unscathed.
To restore your faith in humanity, have a look at the Songs page at Snopes.com, the urban legends website. There you will find links to a number of pages that discuss song origins and related topics. It may raise your spirits to learn that Bob Dylan didn't steal Blowin' In The Wind from a high school student.
Before the age of mass communication and copyright law, none of this was much of an issue. Folk songs were by definition fair game, and blues artists routinely recycled traditional and contemporary material: that was part of their art.
The likes of Bach, Vivaldi and Handel happily nicked bits and pieces from each other, probably seeing it as a dip of the ol' lid to a fellow composer. (To get an idea of the extent of this in classical music, see the long annotated bibliography of Musical Borrowing at the University of Indiana.)
A songwriter's defence could be that there must be a finite number of possible tunes, so it would be surprising if there were no overlap among the millions of songs that have been written. On the other hand, one brave soul at Everything2.com has attempted to calculate that number, and it turns out to be a very big number indeed.
Still, when you consider all the songs and jingles and soundtracks and people whistling a tune in the street that a songwriter hears in a lifetime, it must be maddeningly easy to recycle a snatch of melody without realising it. Then someone hears your latest punk anthem and says, "Hang on, isn't that Dance of the Sugar Plum Fairies?"
It can happen to anyone: browse the Google search results for plagiarism + "George Harrison". You can also read about the cases of Jerome Kern, Britney Spears, Michael Bolton and others listed at the Columbia Law School's Music Plagiarism Project . In the Tin Pan Alley era, songwriter Ira Arnstein became a serial filer of plagiarism suits against his contemporaries, no doubt aided by the fact that it if you set your mind to it, you can find similarities between songs.