Euthanasia is always a last resort - some who are going to die of a terminal illness that is slow and painful choose euthanasia over that, whereas with depression and other mental illnesses there are cures and you have a chance to recover - through therapy and/or medication.
There's a lot of moral issues with euthanasia, and when it is appropriate, and when it comes down to it most people have very different and usually strong opinions.
In my personal opinion, if someone has no quality of life and no chance of recovery, I personally believe that it is appropriate.
As far as I am aware, it is possible to travel to some places in the US and elsewhere for euthanasia, although I am sure many places have strict procedures and policies for who qualifies for euthanasia and who does not. From what I have heard, therapy is also required before the procedure to access your mental state.
Here is a link as to where it is legal. I strongly advise that you only consider this as a last resort, and if you are needing support for mental illness there are always places can be contacted in your general area.
Mental health hotlines in the US