Research
There is a wealth of evidence that homeopathy works, below is just a small selection of links from Nancy Malik's collation of research papers which can be seen in full at http://drnancymalik.wordpress.com/article/scientific-research-in-homeopathy/
Chronic Fatigue Syndrome
More people in the homeopathic medicine group showed clinical improvement on all primary outcomes.
http://www.ncbi.nlm.nih.gov/pubmed/15016577
Otitis media in children
Evidence showed a significant decrease in symptoms at 24 and 64 h after treatment in favor of homeopathy.
Fibromyalgia
Participants on active homeopathic treatment showed significantly greater improvements in tender point count and tender point pain, quality of life, global health and a trend toward less depression.
Patients did better in all variables when they took active (homeopathic) treatment compared to placebo. The improvement experienced by our patients while receiving active treatment was at least as great as that reported for any other treatment that has been assessed double blind.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1837216/pdf/bmj00244-0034.pdf
For an article about one person's experience of homeopathic treatment of fibromyalgia see http://www.britishhomeopathic.org/hh_article_bank/conditions_f_to_l/fibromyalgia_emily_maguire.html
Chronic Obstructive Pulmonary Disorder (COPD)
Tracheal secretions were significantly reduced, with shorter length of stay in the homeopathically treated group.
http://chestjournal.chestpubs.org/content/127/3/936.full
Sports and other physical injuries
For a good discussion on the use on homeopathy in sports see http://www.pponline.co.uk/encyc/homeopathy-in-sport-1075
Plantar fasciitis: resolution of plantar fasciitis appeared to be faster and more complete by the end of the study in the active remedy group than in the placebo group.
Osteoarthritic pain: homeopathic treatment appears at least as effect as acetominophen (paracetomol).
http://www.nationalcenterforhomeopathy.org/content/osteoarthritic-pain-a-comparison-of-homeopathy-and-acetaminophen
Long distance running: hoemopathy significantly reduced muscle soreness at the end of the Oslo marathon.
http://www.sciencedirect.com/science/article/pii/S0965229998800782
Knee surgery: homeopathy reduced swelling following knee surgery
http://www.journals.elsevierhealth.com/periodicals/yctim/article/S0965-2299%2806%2900041-0/abstract
Tendon injury: homeopathy more effective than diclofenac in treatment of tendon injury.
http://www.ncbi.nlm.nih.gov/pubmed/16781589
Musculoskeletal injuries (sprains/strains/bruising): resolution of injury occurred in a higher proportion of the homeopathic treatment group than in the convetional treatment group.
http://www.complementarytherapiesinmedicine.com/article/S0965-2299%2807%2900044-1/abstract