Given the levels of dilution used, and the fact that 18 grams of water (about one tablespoon) contains about 6 × 1023 molecules, this means that homeopathic medicines generally contain zero molecules of the active ingredient – that is, they are generally plain water. The 10:23 anti-homeopathy campaign is based on that idea:
Last year, the Australian National Health and Medical Research Council (NHMRC) completed a review of the effectiveness of homeopathy, concluding that there are no health conditions for which there is reliable evidence that homeopathy is effective because no good-quality, well-designed studies with enough participants for a meaningful result reported either that homeopathy caused greater health improvements than placebo, or caused health improvements equal to those of another treatment.
See also a blog post by the report chair here, or listen to this interview with Edzard Ernst, former Professor of Complementary Medicine at Exeter. XKCD makes an economic argument about effectiveness: