A great article about Terri Schiavo's case, and the Pope's recent remarks about the care of PVS patients, recently appeared on Catholic Exchange.
It's titled "The Case of Terri Schiavo", and gives a concise but thorough discussion of what our moral duty is in such cases:
[S]ociety must not lose sight of the human dignity of the individual, even if diagnosed as being in a "persistent vegetative state." Such a person deserves the same care as anyone else. The pope affirmed the following principles, which uphold the dignity of the sick person: First, the sick person, even if diagnosed as being in a persistent vegetative state, has a right to basic health care (nutrition, hydration, cleanliness, warmth, etc.). Second, he has a right to treatment to prevent complications related to his confinement in bed. Third, he has the right to appropriate care for rehabilitation, and to be monitored for signs of recovery; one must never give up hope of at least a partial recovery (no. 4).
The author, Fr. William Saunders, is a priest of the Diocese of Arlington, Virginia, a professor at the Notre Dame Graduate School of Christendom College, and an all around smart guy. It's well worth reading anything he writes.