Someone mentioned semantics. Good.
Do we have the "right" quite clearly states the premise. A 'right' can only be given to us. By whom?
By laws or gods?
If this had been phrased, "Do we have a CHOICE?" there would have been no question.
Those who speak about the 'gift' of life, our responsibilities to others, the punishment for 'suicide' have no idea in the world how it would feel to be in unbearable physical pain, connected to tubes, catheters, would desire a far more swift death than the one they face.
If such a person has room at all, to 'care' about friends or family, and the agony they also go through in these extended deaths, it is a noble, rational thing to end it swiftly.
The issue of abortion here, is as irrelevant as many of the other comments.
Just suffer and scream because that is what your deity, or the law DEMANDS.
No thanks.
EDIT:
Jake: "Even in terms of euthanasia I would argue that you don't legally have the right to kill yourself, only because it would become quite a hassle to investigate every single euthanasia, because you know there will be some spoiled sons and daughters that would kill their parents for their money under the guise of euthanasia. It's the "Can of Worms" argument."
No, it's the "slippery slope" concept. Any humane advancement can be abused, thus, never make them? How would they 'kill' their parents? Euthanasia would be carefully monitored. Doctors would not simply pull the plug at the request of a relative. In fact, those who assist those who WANT to die, simply give them the means, but do not administrate it.