Alex, the answer to your question is yes, there are scientific studies of homeopathic remedies. For example, a meta-analysis of Clinical trials of homeopathy was published in the British Medical Journal in 1991. (A meta-analysis is a review of a large number of clinical trials on a given topic in an attempt to arrive at a more scientifically reliable conclusion than could be obtained by any one trial.) In case the link doesn't work, the citation is: Kleijnen J, Knipschild P, et al., Clinical trials of homoeopathy. BritMedJ 302(1991):316-23. Most of the trials studied showed a positive effect, and none had a negative effect. And here is a site with a number of more recent clinical trials of homeopathy published in reputable medical journals, with links to more, all found through the PubMed service of the National Library of Medicine.

These studies use good scientific methods (admittedly, more so in recent years than in the past--but that's also true of some standard medical research). The results are often quite impressive, even though the underlying theory doesn't seem to make sense in the context of Western scientific medicine.

Aloha,
Mark