For a clear-cut answer:
If I am going to post the article on several of my websites, yes - I edit them to the point that they become unique.
In this Pandamonium, you don't want to be hit by the slap again. This is why we are on sub-domains now. Making the article unique is more important than ever.
Plus, Google has already said that if any of its products is found to be linked with plagiarism and/or copied content, the Google product is withdrawn from the one that violates it. So, your AdSense account is in danger. Now you might say its written by you, but not only yours, but the ads of those revenue sharing sites are also displayed in your content. They might ban you for placing their AdSense account in jeopardy.
Yes, it is very necessary in this SEO and online world. Its not necessary if you're publishing an e-book or in a newspaper/magazine.