New Thought is an umbrella term for a variety of people and groups who promote positive thinking and the Law of Attraction. One of the most (in)famous examples is in the movie/book The Secret.
The Law of Attraction claims that we attract everything we have in our lives, for good or ill. If you're at all familiar with the self-help industry, you've probably heard this claim before. You may even have an acquaintance who talks about "manifesting" or "putting something out to the Universe."
I have a friend who's really on a kick with this stuff, so I decided to read up on it. I even watched The Secret. The movie makes some pretty outlandish claims, although they're in line with the Law of Attraction if you take it to its logical conclusion. For example, some of the commentators in the movie talk about how people both attract and cure illnesses with their thoughts. Another commentator says that once you master the Law of Attraction, the universe becomes your catalog.
While these claims sound absurd on their faces, I want to address them. Even with the most ridiculous ideas, I think it's important to say why they're actually ridiculous. It's satisfying to dismiss something out of hand because it sounds silly, but many world-changing ideas started out sounding silly, so I prefer to deal with ideas on their own terms.
New Thought actually has some ideas in common with well-known Hindu/Vedanta teachings. Both groups discuss karma and reincarnation. Both groups discourage identification with the physical body and encourage affirmation of positive ideas. For a Vedantic perspective, I recommend this article, particularly the section "Assert Yourself," by Swami Swahananda of the Ramakrishna Order (full disclosure: this is the organization behind the various Vedanta Societies).
Swami doesn't make claims as bold as in The Secret. In fact, I'm pretty sure Vedanta would discourage the idea of treating the universe as a catalog, since it goes against principles such as nonattachment. You might disagree with Swami's ideas about Spirit and Divinity, but I think the worst you can say about them is that they're unprovable.
If it's true that we attract everything into our lives, that implies some serious victim blaming when bad things happen. Of course, just because an idea is harsh doesn't mean it isn't the truth. However, this article in the New York Times implies that scientific validation for the power of positive thinking doesn't look good. I wouldn't be surprised if some of the benefits could be attributed to the placebo effect.
All that said, I do think that state of mind matters, but not in the sense that you can make the universe your catalog (can you tell that this idea really bothers me?). Psychological approaches such as cognitive behavioral therapy focus on changing the way you think about situations, and they can be helpful. I can definitely think of instances in my life where changing my attitude about a situation ultimately changed the situation. However, the attitude change was what was important; the situational change was incidental.
This is where I think The Secret really gets it wrong. The commentators put a lot of emphasis on results, and I think that misses the point. I think the real benefit of a positive attitude is the ability to adapt to whatever situation life throws at you. Have a positive attitude, even visualize what you want, but don't forget to put in some hard work, and know that getting what you want often has less bearing on your happiness than your ability to adapt.