It's a tricky one. The human evidence is scant, as the placebo effect clouds the results. Certainly I've never had any luck with homeopathic remedies despite my doctor being enthused by them. The basis on which they are reputed to act requires a leap of faith, as it really is not scientific. This doesn't mean that they don't work, it's just that if they do we can't explain it. Also the ailments on which they work best are those which are notoriously susceptible to spontaneous remission or improvement, such as allergies, arthritis (particularly rheumatoid), psychological disorders etc. etc. and so anecdotal evidence is difficult to interpret.
The upshot of this is that if you believe in them they are far more likely to work, as an adjunct to traditional therapies they will do no harm at all and as a first try for children suffering from minor ailments they probably are worth a go.
My only real problem with them is the cost: sugar and water just shouldn't be that expensive.