If there were a scientific study that showed that homeopathic remedies had an efficacy better than placebo, I would be embarrassed and proclaim to all that I was wrong. But there is no such study. The British Journal of Clinical Pharmacology produced a paper called "A systematic review of systematic reviews of homeopathy." From the abstract:
Seventeen articles fulfilled the inclusion/exclusion criteria. Six of them related to re-analyses of one landmark meta-analysis. Collectively they implied that the overall positive result of this meta-analysis is not supported by a critical analysis of the data. Eleven independent systematic reviews were located. Collectively they failed to provide strong evidence in favour of homeopathy. In particular, there was no condition which responds convincingly better to homeopathic treatment than to placebo or other control interventions. Similarly, there was no homeopathic remedy that was demonstrated to yield clinical effects that are convincingly different from placebo. It is concluded that the best clinical evidence for homeopathy available to date does not warrant positive recommendations for its use in clinical practice.
A link to the paper:
http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2125.2002.01699.x/abstract;jsessionid=CDEB82CE8023027195DDFF2B09771112.d03t01?systemMessage=Wiley+Online+Library+will+be+disrupted+on+31+August+from+10%3A00-12%3A00+BST+%2805%3A00-07%3A00+EDT%29+for+essential+maintenance
There are lots of other scientific studies that show the same result. The effects of homeopathic remedies are statistically indistinguishable from placebo. Again, this is just about the dilute-and-shake homeopathic remedies, not herbal remedies or supplements. Plenty of natural/herbal remedies are used and used effectively.