Acupuncture works when other means of treatment won't, simply because it works with the body's systems instead of working against them. Drugs usually work by hiding symptoms, instead of healing the underlying cause. For example, nearly every medical condition which ends in ?itis, such as sinusitis, rhinitis and arthritis is an inflammation. These inflammations are normally suppressed by drugs instead of healed/cured.
With the exception of chemotherapy drugs and antibiotics, drugs don't actually lead to a cure. That's why drug companies make so much money ? they have guaranteed repeat business, just like dealers of illegal drugs.
Both modern medicine and Oriental medicine both must work with the natural healing factors of the body to truly affect a cure. The difference is that Oriental medicine almost always works with these healing factors, while modern drugs tend to suppress them. No doctor or therapy can heal even the smallest cut. Only the body has that ability.
Something to consider: Most acupuncturists' largest source of new patients is referrals. This would not happen unless Oriental medicine truly worked.