I'm in favour but only under the condition that
1: The person is suffering from a chronic or terminal illness that causes significant pain/significantly reduced quality of life to the point of eclipsing any chance at a normal life.
2: The person is evaluated by a professional and is considered mentally capable enough to make a decision of that gravity. I personally suffer from Bipolar Disorder and someone like me shouldn't be allowed to make a decision like that. And even then.
3: The decision is made not just by the person in question but also with the consent of a medical professional to ensure that the patient's circumstances warrant such drastic measures.
If even one of those 3 conditions are even a little bit shaky, then I don't think the person should be given access to euthanasia.