Chiropractors vary a lot. Some will claim to be able to treat non-back related conditions such as asthma, infant colic, headaches and a whole plethora of assorted ailments. Multiple reviews show that chiropractic is not effective in treating conditions such as this and so it would be unwise to visit a chiropractor for one of these conditions. Chiropractors which claim to be able to treat these conditions are generally loonies.
However there are systematic reviews which suggest that spinal manipulation can help with back pain to a minor degree. This should only be done after conventional treatments (physio/NSAIDs etc) have been tried and on the advise of a GP. They are expensive so it generally isn't worth pursuing it if you don't feel any benefit after a few sessions.
The evidence is largely inconclusive for neck pain, and manipulation of cervical vertebrae can be dangerous so chiropractic treatment of neck pain is best avoided.
The causes of back pain are incredibly complex and there is no single wonder treatment, it is a matter of finding how best to manage it through the various options.