Blogging at its best is a conversation-between a writer and her readers and among writers passionate about the same topic.
People blog because they want to be part of the conversation, not because they want to be dragged into court.
Nevertheless, bloggers and other writers face two potential land mines when we use other people's words.
If we try to pass off those words as our own, we're guilty of plagiarism.
If we step on the rights of whoever owns the words, we're infringing on their copyright.
The solution to plagiarism is clear and simple: Always, always give people credit for their own words.
A blogger who plagiarizes is going to get caught; all it takes is a quick Google search.
Even if the idea of stealing someone else's hard work doesn't bother you, the inevitable hit to your reputation (and potentially to your pocketbook) should.
The solution to copyright infringement is a little more complex, but still fairly straightforward.
The Copyright Act makes clear there are some cases where we can use someone else's words, calling out such purposes as criticism, comment, news reporting, and research by name.
The legal use of someone else's work is known as "fair use," and the law lays out four guidelines for judging whether something is fair use:

1. the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
2. the nature of the copyrighted work;
3. the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
4. the effect of the use upon the potential market for or value of the copyrighted work.
   (17 U.
   S.
   C.
   § 107)

The Electronic Frontier Foundation expands on these guides in its Bloggers' Legal Guide, noting, among other things, that

• Transformative uses (e.
  g.
  , using the quote to further a conversation) are safer than simply quoting someone,
• Non-commercial uses are safer than commercial ones,
• Quoting published, factual material is safer than quoting unpublished, creative material,
• Quoting little bits is safer than quoting lots of material,

The EFF also notes that the effect on an original's market or potential market is likely to be key:

This factor is often held to be the most important in the analysis, and it applies even if the original is given away for free.
If you use the copied work in a way that substitutes for the original in the market, it's unlikely to be a fair use; uses that serve a different audience or purpose are more likely fair.

So don't shy away from using quotes in your blog.
If you're honest about moving the conversation forward and you're careful about how you use quotes, you should be OK.