Some people will want you to believe that duplicate content is a bad thing, according to Matt Cutts of Google, having duplicate content will not effect you negatively, however google will only count the original publisher of the content.

A prime example was when we distributed a press release back in July. The press release was originally published on Tech Companies Head South To Silicon Beach Miami the article was then distributed and almost 300 media outlets picked up the story. Broadcasters such as CBS, NBC, FOX and others.

If you search google for the title or any of the text in the story you will see that our website is first and always shows, and not the 300 or so media outlets that ran the story.
Now if we had let a publisher in this case a television station publish the article first they would be getting all of the credit and not that of our website.
You want to always publish on your website or blog first, and check to make sure google has indexed your article or story before sharing it.

Question originally asked on http://www.quora.com/Does-republishing-content-on-other-blogs-hurt-the-SEO-Do-you-rewrite-or-copy-paste-your-posts