In some cases, the original artist or his/her representatives objected to the appropriation, and actually threatened or initiated legal action. The "Sweet Little Sixteen"/"Surfin' USA" dispute was settled relatively quickly, as was another dispute that I will get to shortly. On the other hand, the "He's So Fine"/"My Sweet Lord" dispute involved twenty years of litigation.
In some cases, the original artist provided no comment on the appropriation. Most notably, Ludwig van Beethoven never provided a comment on Electric Light Orchestra's version of "Roll Over Beethoven." In its original form (another Chuck Berry song, by the way), the song only mentioned Beethoven, but by the time ELO recorded it, a significant excerpt from the Fifth Symphony had been included. Not that Beethoven cared. (Not only had Beethoven expired by the time "Roll Over Beethoven" first appeared, but his copyright had expired also.)
In some cases, the original artist was a willing participant in the appropriation. Daft Punk has actually appeared on stage with Kanye West when West has performed "Stronger," his version of "Harder, Better, Faster, Stronger."
But there's one thing that unites all of these new versions of old songs. In my opinion, these new versions are better than the originals. Vocally, the Beach Boys blew Chuck Berry out of the water, and the instrumentation was more inventive. And while I have personal problems (religious issues) with Harrison's lyrics, I love his guitar work from that period. "Roll Over Beethoven" has been recorded in many different versions, but the one from the Electric Light Orchestra stands out as a successful attempt to marry classical and rock music. And Kanye (while I again have issues with some of the lyrics) is a much better singer than the Dafts, and again he provides better instrumentation.
But my best example of a re-visitation being better than the original was Kelly Osbourne's take on Viisage's "Fade to Grey." Her version is called "One Word," and while Viisage certainly had a notable take on the song, Osbourne's beats the original.
In my opinion.