[All things that have been discussed here before, but some people wanted it all in a convenient place]
The most important study on the placebo effect is Hróbjartsson and Gøtzsche's Is The Placebo Powerless?, updated three years later by a systematic review and seven years later with a Cochrane review. All three looked at studies comparing a real drug, a placebo drug, and no drug (by the third, over 200 such studies) – and, in general, found little benefit of the placebo drug over no drug at all. There were some possible minor placebo effects in a few isolated conditions – mostly pain – but overall H&G concluded that the placebo effect was clinically insignificant. Despite a few half-hearted tries, no one has been able to produce much evidence they're wrong. This is kind of surprising, since everyone has been obsessing over placebos and saying they're super-important for the past fifty years.