Now before you go thinking that i'm going to be all negative on the subject, i'll start by saying that i think the placebo effect is highly underrated. If someone was to tell you that in a reasonable number of cases a sugar pill could be as effective in treating illnesses as an expensive medication you'd be pretty impressed. You might even ask why we don't try to treat everything with sugar pills instead of spending lots of money on pharmaceuticals. Alas the placebo per se doesn't do anything and the effect relies on the patient believing the sugar pill will improve their condition, therein lies the link to positive thinking.
I suspect that most of the cynicism about 'positive thinking' is based on the screeds of pseudo-scientific books which propose a variety of far-fetched mechanisms for how it works from auras, to spirits or even quantum mechanics. Some of these mechanisms are occasionally covered in a thin veneer of real science (yes, there is a zero point field) but invariably the mechanism cannot be scientifically proven (there is no hard evidence to indicate that people can manipulate the zero point field with their thoughts). On the other hand there are a number of scientifically proven theories which can shed some light on the benefits of thinking positively.
Psychological - This one is obvious, if you frame everything in a positive light you will be happier; threats become opportunities, something going wrong becomes a chance to do something different. It doesn't take a genius to see that if you choose to perceive things in a positive way you will feel more positively about things, it's simple tautology (circular logic). Furthermore there are a number of cognitive biases which are likely to amplify the feeling that if you think good thoughts, good things happen. The most relevant in this case is Confirmation Bias; "the tendency to search for or interpret information in a way that confirms one's preconceptions.". In other words if you believe something, you are more likely to accept evidence that agrees with your belief and ignore evidence which does not agree with your belief. So if you think positively and believe it makes your life better, you will be more inclined to notice and remember positive things that happen and dismiss any negative things that happen. Now if you want to make optimal decisions or become a being of pure reason and logic, tautology and cognitive bias are to be avoided. On the other hand if you want to be happy, thinking positively is bound to help.
Physiological - Thinking comes from the brain, the brain controls a lot of the processes in the rest of the body, so there could be a link between positive thinking and physical wellbeing. Please don't ask me to dig up the research, but there is ample evidence linking mental state with physiological effects. One example is that if you are stressed (a mental state), your brain triggers your adrenal gland to release cortisol (a physiological response). Now in some ways cortisol is great; in the short term it helps you metabolise protein, carbohydrates and fat, which is pretty useful if you are stressed because you are being chased by a tiger. On the other hand in the long term it suppresses your imune system and slows bone growth, both of which are less than ideal. I don't propose that we fully understand how mental state effects physiology. However given that your brain regulates a large number of hormones and systems, from an evolutionary standpoint there is a good chance that being happy and relaxed is better for you than being depressed and stressed.
Interpersonal - So the above covers why thinking positively can be beneficial to your mental state and physical wellbeing, but if it doesn't translate beyond you as an individual then it is borderline delusion. Fortunately there is scientific evidence which supports emotions - and hence positive thinking - being contagious between people. Let's try an experiment; the next time you are outside, smile at a random person. Nine times out of ten they will smile back, unless of course they are in a really shitty mood. While that of itself is quite impressive, what is even more impressive is that by the mere action of smiling that person will feel slightly happier. This reciprocation is caused by mirror neurons in the brain, you don't just mirror movements but emotions as well. There is no need to invoke spirits or psychics or quantum mechanics, it is simply neurobiology. Humans are social creatures and have been long before the advent of language, it makes sense that our ancestors would have had an evolutionary advantage if they could understand and influence other individuals. So if you think positively and are therefore happier, that happiness/positivity is likely to rub off on people you meet, which will result in better outcomes from those interactions.
The three paragraphs above are my best attempt at remembering and summarising the science at 3am after a few beers. The examples are limited, the explanations imperfect and they are distinctly lacking in citations. If you would like more detailed information on anything above, or suggested reading, please leave a comment.
Conclusion - Do i think that peoples positive vibes somehow propagate out through the zero point energy field and change the universe? Or that you can manifest a new Lexus by thinking positive? Hell no. On the other hand i do think that there is good scientific evidence for why people with a positive outlook on life are happier, healthier and have better relationships.
Some related Wikipedia links:
The Placebo Effect
Physiological Effects Of Cortisol
List of Cognitive Biases