Some of the more common request are for general well-being, pain control, stress, fertility, migraine, skin disorders, depression, anxiety, and addictions.
The British Acupuncture Council has produced some facts sheets detailing some of the research that has been published on some common conditions treated by acupuncture. There is a link on the left hand side -facts sheets.

whoThe World Health Organisation has produced a guide regarding acpuncture  here is a summary if you want to read to complete report (87 Pages ) click here

This information was taken from the Website of the World Health Organisation The document was published in 2002 and gives their own opinion on using Acupuncture for specific conditions.

3. Disease and disorders that can be treated with acupuncture

3. Diseases and disorders
that can be treated with acupuncture The  diseases  or  disorders  for  which  acupuncture  therapy  has  been  tested  in controlled clinical trials reported in the recent literature can be classified into four categories as shown below.

1.Diseases,  symptoms  or  conditions  for  which  acupuncture  has  been  proved—through controlled trials—to be an effective treatment:
Adverse reactions to radiotherapy and/or chemotherapy
Allergic rhinitis (including hay fever)
Biliary colic
Depression (including depressive neurosis and depression following
Dysentery, acute bacillary
Dysmenorrhoea, primary
Epigastralgia, acute (in peptic ulcer, acute and chronic gastritis, and
Facial pain (including craniomandibular disorders)
Hypertension, essential
Hypotension, primary
Induction of labour
Knee pain
Low back pain
Malposition of fetus, correction of
Morning sickness
Nausea and vomiting
Neck pain
Pain in dentistry (including dental pain and temporomandibular
Periarthritis of shoulder
Postoperative pain
Renal colic
Rheumatoid arthritis
Acupuncture: review and analysis of controlled clinical trials
Tennis elbow

2. Diseases,   symptoms   or   conditions   for   which   the   therapeutic   effect   of acupuncture has been shown but for which further proof is needed:
Abdominal pain (in acute gastroenteritis or due to gastrointestinal spasm)
Acne vulgaris
Alcohol dependence and detoxification
Bell’s palsy
Bronchial asthma
Cancer pain
Cardiac neurosis
Cholecystitis, chronic, with acute exacerbation
Competition stress syndrome
Craniocerebral injury, closed
Diabetes mellitus, non-insulin-dependent
Epidemic haemorrhagic fever
Epistaxis, simple (without generalized or local disease)
Eye pain due to subconjunctival injection
Female infertility
Facial spasm
Female urethral syndrome
Fibromyalgia and fasciitis
Gastrokinetic disturbance
Gouty arthritis
Hepatitis B virus carrier status
Herpes zoster (human (alpha) herpesvirus 3)
Labour pain
Lactation, deficiency
Male sexual dysfunction, non-organic
Ménière disease

3. Disease and disorders that can be treated with acupuncture

Neuralgia, post-herpetic
Opium, cocaine and heroin dependence
Pain due to endoscopic examination
Pain in thromboangiitis obliterans
Polycystic ovary syndrome (Stein–Leventhal syndrome)
Postextubation in children
Postoperative convalescence
Premenstrual syndrome
Prostatitis, chronic
Radicular and pseudoradicular pain syndrome
Raynaud syndrome, primary
Recurrent lower urinary-tract infection
Reflex sympathetic dystrophy
Retention of urine, traumatic
Sialism, drug-induced
Sjögren syndrome
Sore throat (including tonsillitis)
Spine pain, acute
Stiff neck
Temporomandibular joint  dysfunction
Tietze syndrome
Tobacco dependence
Tourette syndrome
Ulcerative colitis, chronic
Vascular dementia
Whooping cough (pertussis)

Diseases,   symptoms   or   conditions   for   which   there   are   only   individual
controlled  trials  reporting  some  therapeutic  effects,  but  for  which  acupuncture
is  worth  trying  because  treatment  by  conventional  and  other  therapies  is
Choroidopathy, central serous
Acupuncture: review and analysis of controlled clinical trials
Colour blindness
Irritable colon syndrome
Neuropathic bladder in spinal cord injury
Pulmonary heart disease, chronic
Small airway obstruction

Diseases, symptoms or conditions for which acupuncture may be tried provided
the   practitioner   has   special   modern   medical   knowledge   and   adequate
monitoring equipment:
Breathlessness in chronic obstructive pulmonary disease
Convulsions in infants
Coronary heart disease (angina pectoris)
Diarrhoea in infants and young children
Encephalitis, viral, in children, late stage
Paralysis, progressive bulbar and pseudobulbar