From Evangelium Vitae (65, 97):

“The work of education cannot avoid a consideration of suffering and death. These are a part of human existence, and it is futile, not to say misleading, to try to hide them or ignore them. On the contrary, people must be helped to understand their profound mystery in all its harsh reality. Even pain and suffering have meaning and value when they are experienced in close connection with love received and given. In this regard, I have called for the yearly celebration of the World Day of the Sick, emphasizing the salvific nature of the offering up of suffering which, experienced in communion with Christ, belongs to the very essence of the Redemption.  Death itself is anything but an event without hope. It is the door which opens wide on eternity and, for those who live in Christ, an experience of participation in the mystery of his Death and Resurrection."
 

From On Artificial Nutrition & Hydration from the the Offices of the Congregation for the Doctrine of the Faith

Euthanasia must be distinguished from the decision to forego so-called aggressive medical treatment, in other words, medical procedures which no longer correspond to the real situation of the patient, either because they are by now disproportionate to any expected results or because they impose an excessive burden on the patient and his family. In such situations, when death is clearly imminent and inevitable, one can in conscience refuse forms of treatment that would only secure a precarious and burdensome prolongation of life, so long as the normal care due to the sick person in similar cases is not interrupted. Certainly there is a moral obligation to care for oneself and to allow oneself to be cared for, but this duty must take account of concrete circumstances. It needs to be determined whether the means of treatment available are objectively proportionate to the prospects for improvement. To forego extraordinary or disproportionate means is not the equivalent of suicide or euthanasia; it rather expresses acceptance of the human condition in the face of death.”
 

From Evangelium Vitae (66):

“To concur with the intention of another person to commit suicide and to help in carrying it out through so-called "assisted suicide" means to cooperate in, and at times to be the actual perpetrator of, an injustice which can never be excused, even if it is requested. In a remarkably relevant passage Saint Augustine writes that "it is never licit to kill another: even if he should wish it, indeed if he request it because, hanging between life and death, he begs for help in freeing the soul struggling against the bonds of the body and longing to be released; nor is it licit even when a sick person is no longer able to live".85  Even when not motivated by a selfish refusal to be burdened with the life of someone who is suffering, euthanasia must be called a false mercy, and indeed a disturbing "perversion" of mercy. True "compassion" leads to sharing another's pain; it does not kill the person whose suffering we cannot bear. Moreover, the act of euthanasia appears all the more perverse if it is carried out by those, like relatives, who are supposed to treat a family member with patience and love, or by those, such as doctors, who by virtue of their specific profession are supposed to care for the sick person even in the most painful terminal stages.
 

From Evangelium Vitae (65):
“For a correct moral judgment on euthanasia, in the first place a clear definition is required. Euthanasia in the strict sense is understood to be an action or omission which of itself and by intention causes death, with the purpose of eliminating all suffering. "Euthanasia's terms of reference, therefore, are to be found in the intention of the will and in the methods used…

Taking into account these distinctions, in harmony with the Magisterium of my Predecessors and in communion with the Bishops of the Catholic Church, I confirm that euthanasia is a grave violation of the law of God, since it is the deliberate and morally unacceptable killing of a human person. This doctrine is based upon the natural law and upon the written word of God, is transmitted by the Church's Tradition and taught by the ordinary and universal Magisterium.”