Patient of the Week

In a Medical Drama the patient has a disease that is the focus of the episode, with a little personal drama thrown in. This is the Monster of the Week construction, Medical Edition.

Live Action TV

 * House - Arguably justified, in that the show is based on the premise that House and his team only take patients who have been examined by multiple other doctors and are still missing a diagnosis. Deconstructed in several episodes; once when new administrator Edward Vogler wanted to fire House because only treating one patient a week isn't cost-effective, and again when House confessed to a patient that he chooses to take only one case at a time, often leading to unfortunate results for the twenty-odd files he passes up. The show also deviates from the formula comparatively often.
 * ER - possibly justified, as it's set in an emergency room, where it's expected that patients are either cured, killed, or moved to another department. Doesn't explain why they usually only have one patient a week, though.
 * Fellow Medical Drama Greys Anatomy follows this trope almost religiously, only deviating from it on special occasions. Typically, the cast will split into halves (or thirds, or fourths, depending on how many subplots are the episode has), each group tackling a single patient who'll provide some perspective or wisdom that can be easily applied to whatever problem a character has, then disappear and never be heard from again.
 * Casualty - Characters will show up with horrendous injuries and be diagnosed/cured within the space of one afternoon. Then they never appear again, no matter how interesting, and about half of the next episode is devoted to the introduction of a new Patient of the Week. Like ER, it is set in an A&E department.
 * Casualty Spin-Off Holby City also uses the Patient of the Week format - while it's not as frequent as in the parent show, the fact that Holby City is set in a cardiac surgery department makes it rather more inexplicable.
 * Scrubs, though it's not as bad as the others.
 * That's because Scrubs isn't a medical mystery show. It is a work comedy that centers purely on the doctors. The patients only show up when it's plot important. It's very apparent that they wanted to stand out from the others.
 * MASH: shows up at least a few times a season. Justified since the point of a field hospital isn't to monitor patients long-term but to get them either fit for duty or stable enough to transport away from the war zone, and also subverted with episodes that feature large numbers of patients and illustrate the necessity of triage.
 * In Doctors, the doctors ended up solving their patients' life troubles so often that the writers started having people seek them out for psychological aid.