Placebos work in general as long as the problems are psychological. The whole field Chinese Medicine depends on that.
There was a study [0] about the placebo effect in heart failure patients: "In a 1999 Swedish Study, doctors implanted an active pacemaker into 40 heart failure patients. Another 40 patients underwent the same surgery, believing they were receiving active pacemakers. But their pacemakers were never turned on: they were, in essence, placebo pacemakers." - [1]
Now as a disclaimer, I did not complete read or understand this study nor do I know if there are counter studies, but it's my favorite bit of information about the placebo effect.
[0] http://www.ncbi.nlm.nih.gov/pubmed/10190407
[1] http://blog.placeboeffect.com/reverse-heart-disease/ (laymen conclusion)