From the World Health Organization’s list of conditions recommended for Acupuncture :

Acute sinusitis
Acute rhinitis
Common cold
Acute tonsillitis
Bronchopulmonary Diseases
Acute bronchitis
Bronchial asthma
Eye Disorders
Acute conjuctivitis
Cataract (without complications) Myopia
Central retinitis
Disorders of the Mouth Cavity
Toothache Pain after tooth extraction Gingivitis Pharyngitis
Orthopedic Disorders
Periarthritis humeroscapularis
Tennis elbow
Sciatica
Low back pain
Rheumatoid arthritis
Gastrointestinal Disorders
Spasm of the esophagus and cardia
Hiccups
Gastroptosis
Acute and chronic gastritis
Gastric hyperacidity
Chronic duodenal ulcer
Acute and chronic colitis
Acute bacterial dysentery
Constipation
Diarrhea
Paralytic ileus
Neurologic Disorders
Headache
Migraine
Trigeminal neuralgia
Facial paralysis
Paralysis after apoplectic fit
Peripheral neuropathy
Paralysis caused by poliomyelitis
Meniere’s syndrome
Neurogenic bladder dysfunction
Nocturnal enuresis
Intercostal neuralgia

Link to World Health Organization Full Report