Many blogs and websites encourage you to copy and link to their material. However, mainstream media may specifically rule out posting their content elsewhere. The L.A. Times says personal use does not include posting to a website and the Houston Chronicle says “no reproduction except for limited personal use.” So while fair use might mean you can quote from them (and lots of blogs do just that) be aware they could consider doing so to be copyright infringement and they have lots of lawyers and you probably don’t. Also both newspapers are owned by large media companies so it’s probably safe to say these are company-wide policies. However, their company policy of no quoting is just that, policy, while fair use is law.
EFF has an informative Bloggers’ FAQ on Intellectual Property. Highlights include the following. Facts and ideas are ok to copy, the way they are expressed is what is copyrighted. Anything from a government document can be copied. Parody is a type of fair use. Satire, which uses the quoted material to mock something else is not as protected.
Blogs in general, want you to copy their text and link to them. That’s what blogging is about. Just don’t quote huge blocks of text, and always link back to the source. But this isn’t a given, as is nothing in Fair Use.
If you aren’t sure, you can always ask for permission or paraphrase what you want to quote.