It is permissible to wear braces (in order to line teeth as they grow) and doing this is not be a sin. It is not a deemed a "cosmetic reason for beauty" but a medicinal reason to cure an abnormality. If the teeth are left to grow without braces then there is a very high likelihood that they will cause pain and difficulty in later life.
Cosmetic surgery which is undertaken by a normal healthy person for the sake of beautification is not permissible and is changing the way Allah created someone. It is muhla (mutilation) of the human body and as mentioned in the earlier answers, is forbidden.