Darkening of under arms and neck and sometimes inner thighs is very common concern
It is more commonly seen obese persons, diabetics, hypothyroid patients but can occur in anyone and can be rarely caused by drugs and very rarely can be a sign of underlying cancer.
The most common cause for it is acanthosis nigricans which is many times interpreted by patients as just pigmentation.
Correct diagnosis and identifying underlying cause is must for correct treatment.
There are some creams with skin lightening agents which can help and sometime you may need to take oral medicines to reduce weight and darkening both.
Read more:
http://www.mayoclinic.org/diseases-conditions/acanthosis-nigricans/basics/definition/con-20025600
http://www.webmd.com/skin-problems-and-treatments/acanthosis-nigricans-overview
http://emedicine.medscape.com/article/1102488-overview