Among the best new grown-up dramas of the fall season, “Homeland” (9 p.m., Showtime) features a great cast and addictive story. Claire Danes (“Temple Grandin”) stars as obsessive CIA agent Carrie Mathison. She’s convinced that Nick Brody (Damian Lewis, “Band of Brothers”), a recently liberated American POW who had been missing in Iraq since 2003, has been “turned” by his captors and represents a security threat. This runs counter to the agency’s opinion (and well-orchestrated spin) that he is a hero rescued by their diligent efforts.

”Homeland” keeps you guessing. Is Carrie right? Or unstable, desperate and confused? Is Nick a spy, or a man whose memory and identity have been permanently traumatized?

“Homeland” nicely blends this “Manchurian Candidate” theme with a subplot not unlike “Cast Away.” In Nick’s long absence, his wife, Jessica (Morena Baccarin, “V”), has been carrying on a steamy romance with his best pal and fellow Marine. His children barely know him. This domestic tension and marital discord echo Carrie’s creepy surveillance of her prey.

This is a show where nobody can trust anybody else and where the smallest gesture and unanswered phone call can take on great import.

• Documentary filmmaker Ken Burns chose a great subject for his new effort. “Prohibition” (7 p.m., PBS) takes on a 20th-century “experiment” with deep roots in the 19th century and resonant lessons for the 21st. Airing nightly through Tuesday, “Prohibition” devotes Sunday’s episode to the efforts to ban alcohol, a crusade born in the pulpit in the first half of the 1800s, when distilled grains replaced fermented cider. The exponential increase in liquor’s potency reduced many farmers and workingmen to helpless inebriates and left their wives and families brutalized and impoverished. For many Christians and feminists, the issue of temperance was as important as the abolition of slavery.

“Prohibition” asks as many questions as it answers. How did this peculiar amendment come to pass? What are the limits of social engineering? How far can the government go in enforcing “good” behavior before it becomes dictatorial in nature, while at the same time hypocritical and ineffectual?

• Endearing to many, infuriating to some (and endearing to others because he is infuriating), Andy Rooney will say goodbye to “60 Minutes” (6 p.m., CBS).

Tonight’s other highlights

• The Baltimore Ravens host the New York Jets on “Sunday Night Football” (7 p.m., NBC).

• Alicia bones up on English law on “The Good Wife” (8 p.m., CBS).

• Gaby has spicy plans for Carlos on “Desperate Housewives” (8 p.m., ABC).

• Margaret goes undercover to help Nucky in a time of crisis on “Boardwalk Empire” (8 p.m., HBO).

• High school reunions can be murder on the season premiere of “Dexter” (8 p.m., Showtime).

• Male escorts and murder don’t mix on “CSI: Miami” (9 p.m., CBS).

• Rangoon calling on “Pan Am” (9 p.m., ABC).