I think massage helps everything! But, it won't FIX everything.
With chronic pain, massage is an excellent component of a management plan that may include chiropractic adjustments, exercise, lifestyle change, physical therapy, medication and medical treatments.
Here are some conditions that I have found massage addresses very well:
Stress
Rest and relaxation are vital parts of stress management.
Neck/shoulder pain
Work at a computer 8 hours a day? Massage will ease this "my neck is killing me" condition very quickly .... until you go back to the computer for 8 hours.
Sciatic pain
Especially if the pain is caused by a muscle impinging on the sciatic nerve.
Carpal Tunnel symptoms
Particularly if the symptoms are caused by Thoracic Outlet Syndrome.
Migraines
Particularly if the migraine is caused by pain referred from extremely tight muscles in the neck.
Plantar fasciitis
This presents as pain in the heel, most often in the morning.
Torticollis
A neck "crick." More serious issues, like cervical dystonia (spastic torticollis) benefit from massage as part of a multi-disciplined approach to treatment.
TMJ dysfunction
Misalignment of the joint of the jaw can be painful at the joint itself, reduce range of motion and refer pain into the ear, cause headaches.
For some conditions, I've found massage can help as part of an on-going management program:
Multiple Sclerosis
Neuropathy from chemotherapy
PLS (Primarly Lateral Sclerosis)
Dropped head syndrome
Frozen shoulder
Rotator cuff injuries