Euthanasia/Assisted Suicide doesn't always coincide. Euthanasia is commonly known as "mercy killing", and while the two can be the same in some instances and have similarities, they have their differences.
I am against euthanasia unless those trying to assist the person are past the point that they can. If someone is on life support for years and years on end to the point that it eats up their family's financials to the point that they cannot support themselves, it is fine. Same with long term cancer patients who become to tired to keep fighting, only in this case I feel more comfortable with the "let them die" situation more than actually speeding up the process. If in a war/battle a person is injured past the point of recovery and they specifically state they want to be put out of pain, it is also fine- however only by a soldier/civilian, not a doctor..
On the other hand, if it is not the above situations- say a family member is unable to speak for themselves, or are disabled in some way (as some victims of euthanasia are) I would be very much against it. We cannot determine if their lives are worth going on. It is not our place to determine such things.
As for assisted suicide, I agree with it in much of the situations of above. However, if one is simply tired of living and continuing with life, they are just as morally responsible as other suicide victims who harmed their family- no matter the age. They are just (to put it harshly) too cowardly to do it themselves. It's not really a matter of should it be allowed, but rather should others be made to help them. That's the real issue. If doctors have to start assisting with suicide, it violates quite a few bits of patient/doctor trust, as well as doctor's morals to a certain extent. To require someone to assist with another's death is a bit to much. Furthermore, it would become difficult to stop some cases of abuse of that privilege. And even furthermore, it does not change the fact that suicide alone is considered illegal in certain countries, and that adding another into the equation is much like having another person assisting in another crime.